Physics-
General
Easy
Question
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
Find minimum time it will take to reach from
to 0.
- None
The correct answer is: ![square root of fraction numerator m A over denominator F end fraction end root left parenthesis square root of 2 minus 1 right parenthesis](data:image/png;base64,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)
Related Questions to study
physics-
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
![](data:image/png;base64,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)
Velocity – time graph of the particle is
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
Velocity – time graph of the particle is
physics-General
physics-
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
What is the period of the motion?
A particle of mass m is constrained to move on x-axis. A force F acts on the particle. F always points toward the position labeled E. For example, when the particle is to the left of E, F points to the right. The magnitude of F is a constant F except at point E where it is zero. The system is horizontal. F is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position E and released from rest at t = 0.
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)
What is the period of the motion?
physics-General
physics-
A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?
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)
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)
A weight can be hung in any of the following four ways by string of same type. In which case is the string most likely to break?
![](data:image/png;base64,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)
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)
physics-General
physics-
A stunt man jumps his car over a crater as shown (neglect air resistance)
![](data:image/png;base64,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)
A stunt man jumps his car over a crater as shown (neglect air resistance)
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown the velocity of different blocks is shown. The velocity of C is
![](data:image/png;base64,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)
In the figure shown the velocity of different blocks is shown. The velocity of C is
![](data:image/png;base64,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)
physics-General
physics-
Two masses m and M are attached to the strings as shown in the figure. If the system is in equilibrium, then
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)
Two masses m and M are attached to the strings as shown in the figure. If the system is in equilibrium, then
![](data:image/png;base64,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)
physics-General
physics-
Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.
![](data:image/png;base64,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)
Block of 1 kg is initially in equilibrium and is hanging by two identical springs A and B as shown in figures. If spring A is cut from lower point at t=0 then, find acceleration of block in ms–2 at t = 0.
![](data:image/png;base64,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)
physics-General
physics-
Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2 ms–2 as shown in figure.
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)
Find the acceleration of 3 kg mass when acceleration of 2 kg mass is 2 ms–2 as shown in figure.
![](data:image/png;base64,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)
physics-General
physics-
Both the blocks shown here are of mass m and are moving with constant velocity in direction shown in a resistive medium which exerts equal constant force on both blocks in direction opposite to the velocity. The tension in the string connecting both of them will be : (Neglect friction)
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)
Both the blocks shown here are of mass m and are moving with constant velocity in direction shown in a resistive medium which exerts equal constant force on both blocks in direction opposite to the velocity. The tension in the string connecting both of them will be : (Neglect friction)
![](data:image/png;base64,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)
physics-General
physics-
What should be the minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane.
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)
What should be the minimum force P to be applied to the string so that block of mass m just begins to move up the frictionless plane.
![](data:image/png;base64,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)
physics-General
physics-
The equation of a wave disturbance is given as :
where x and y are in meters and t in seconds. Choose the wrong statement:
The equation of a wave disturbance is given as :
where x and y are in meters and t in seconds. Choose the wrong statement:
physics-General
physics-
Four open organ pipes of different lengths and different gases at same temperature as shown in figure. Let fA , fB , fC and fD be their fundamental frequencies then :[Take
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![](data:image/png;base64,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)
Four open organ pipes of different lengths and different gases at same temperature as shown in figure. Let fA , fB , fC and fD be their fundamental frequencies then :[Take
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![](data:image/png;base64,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)
physics-General
physics-
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed
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59OgICAjp1V6coCnq9Hjk5OTAYDODxePDy8mKruw8ePBhOpxNGoxH19fXIz8/HiRMncOLECZw6dQoZGRng8XiQyWSQy+WQy+UICwtD3759ERUVhfDwcISGhkKlUl0zWqd1sWsmla4zGFksFiMmJgbr1q2Dl5cXtm7dihdffBFCoRCzZ8/ukckJf3rmJIQgPT0dL774IqqqqjBnzhwsWbIE3t7eXbLb63Q6fPjhh9i6dSvi4uLw+OOPY+LEiZBKpT1isQgEAqhUKsjlcoSEhCA1NRUOhwMNDQ345ZdfUFBQgKKiItTW1sJgMCA3NxfHjx8HIYQ9MXk8HoRCIbRaLWiahlQqhUwmg0qlglarhZ+fH0JDQxEeHo7w8HD4+Ph0yqbI4/Gg0WiwaNEiAMC2bduwceNGSKVSTJs2rccFKvypmdNqteLEiRNYuXIl9Ho95s2bh3/84x8ICAjokhPTZrNh9+7d2LVrF/r06YOnnnoKY8eOhVwu7xLG5PP5iI+Px8yZM9vUoG0NploCj8eDSCRir2u1WkRFRSE1NRVGoxF6vR56vR41NTVsFXij0QiTyQSbzQaHwwEul4umpibYbDY0Nzfj8uXLbAlNgUDAtnWIiopCZGQkoqKi2Ir1nqipxOFwIBAIEBoaiieeeAI2mw0HDx7Ea6+9BpVKheHDh/eoKKk/rc7pcrlw4cIF/OMf/0BxcTGmT5+Ol19+GTKZrEtOTKvViqNHj2Lx4sXg8Xh4//33kZSU1KVRLIxRyGQyQS6Xe8xdwrhxmELZrXu9tK5ry1SJLygowPHjx5Gbm8uGH4rFYnh7e+Oee+7B0qVLIZfL2eLTnoDL5UJDQwOeeeYZfP311wgLC8M777yDYcOG9ZgTlPfiiy++2N1EdAeKi4uxYcMGHD16FFOmTMFzzz3HWh47+9SiaRoXLlzAk08+Cbfbjcceewx3330328ekq8BsUIcOHYJSqYRWq/XIuIz+yHQrYyKVGH2W0VG1Wi2io6MxfPhw3HfffXjooYcwYsQIhIaGQiqVwmAw4MSJE0hLS0NTUxO8vLwQGBjokVOUy+WyemhzczOysrKg0+lYS3R3G7CAPyFzOp1O1NbW4rXXXsOhQ4eQkpKCF154AeHh4eDz+V0iTtbU1GDTpk3IyMjAlClT8Nhjj3WanvV7sNvt2LVrF1555RUMHjwY/fv399jYravstf4wIjJTuZ6J/ZVIJFCr1YiMjGSLaicmJiI0NBRGo5ENWaysrIRarYaXl1cbMftm6OPxePD29kZsbCxqamqQm5uLsrIyjBgxokvqBl8X3eZh7QZQFEUMBgNZs2YNCQkJIUOHDiVnz57tstQixvm/bt060q9fPzJixAhSWFjYbc5wk8lE1qxZQyQSCfn000+7hYbfA03TxGazkerqarJixQoSFhZGlEolmTRpEjl9+jQxm83E7XZ3+DkOh4OUlZWRqVOnEj8/P7Jo0SKi1+u7PUih+8/uLoTFYsHhw4fx4YcfQqPRYMmSJejfv3+XdbsyGo3YsmUL3n77bXC5XKxbtw5BQUE9wirbE8HhcFgr79KlS7Fjxw5Mnz4dFy9exJw5c7B582YYDIYOP0cgECAwMBCPP/44YmNjsWvXLuzfvx92u90Db3Hz+NOItYQQ5Obm4qWXXoLZbMbTTz+NyZMnd5kBqLm5GSdOnMD69evB4XDwr3/9C3feeWe3V+Tz9vZG//79kZKSAh8fn26j41pgRGOGSRMTEyGRSPDTTz/h5MmTMJlM6Nu3b4cs3IyIyyQSHDhwADqdDv3792d13G5Bt57bXQS3201qa2vJlClTiJ+fH1m+fHmXiS2MKJuZmUlGjRpFfHx8yIoVK4jJZOp2sYmiKGK1WolerydWq7VbaWkPjEYjSUtLI5GRkUSr1ZI5c+aQmpoa4nK5OjQuTdPEYDCQJUuWkODgYHLXXXeRurq6Lomrvhr+FMzZ0NBAnnvuORIUFERuv/12cunSpS6bcJPJRD7//HOSmJhIgoKCyIoVK4her+8RlflsNhvZs2cPmTNnDsnIyOhucm4YzIZ3/PhxMm7cOOLr60sefPBBUlpa2uENz+l0koqKCjJt2jSi1WrJ4sWLSVVVlYcobx/+8EEIJpMJOTk52LlzJ2QyGZ588kmEhYV1iSWuvr4eBw8exIYNG2CxWPDwww9j/vz5UKlUnS5K2+12WCwWWCwW2Gw2tLS0oLq6Gnq9HmazmfVvnj17FmfPnkVLSwsOHz7Muj2kUin8/PwQGBgIpVLJJmz3hPQxLpcLiUSCIUOGYM2aNVixYgV++OEHaLVaPP300x1qZcjn8xEQEID58+ejvLwcu3fvRmJiIqZOndqlCfbAHzwIgaZp/PLLL1i6dClycnKwbNkyPPbYY52aiUD+10Grvr4en3/+OTZu3AiapvHoo49i8eLFnRIWyAQTOJ1OmM1mmEwmlJeXIysrCwUFBbh8+TLq6+tB0zRa/9yEELaiure3NyQSSZv/Z/Q9jUaDPn36oH///hg+fDgiIiIgk8kgk8kgEonYFhPdAbfbjfPnz2PhwoUoKyvD0qVL2d+4IzSZTCZ8+eWXePrppzFo0CC88cYbGDBggAcpvz7+sMxJCIHFYsELL7yAzz77DFOnTsXy5csREhLSqQuJoiiUlZVh9erV2LdvH7y9vfHMM8/gvvvu6xTGZN7z+PHjOHnyJPLy8lBaWgqdTgen08laIvv06YPw8HA2gVosFoOmaWRlZeHw4cO4//77MWjQILZYVktLC3Q6HS5fvoyysjJUVlaCoijw+XwEBgYiMjISCQkJGDlyJEaMGNFtmR2EEFitVmRkZGDRokXg8XhYu3YtJk2a1KF+ozRNo6GhAevWrUNaWhr+8pe/YOPGjV1qHPrDMicTt/rqq6+Cx+Nh8+bNSEhI6DSRjKIoVoReu3YtCgsLERYWhhdeeAHDhg2DTCbzmChtMplQX1+PoqIiZGRk4NSpU9DpdHA4HODz+dBoNBgwYACSk5MRExMDhUIBqVQKqVQKiUQCgUAAHo8HiqLQ0tKC2tpaBAQEQKlUsu/icrlgs9lY0dhsNqOoqAinT5/GTz/9hMbGRrhcLohEIgQGBiI5ORm33XYb+vbtC41G06WVBiiKgsViwVtvvYVt27YhNjYWmzZtQmhoaIfm3G6349KlS3jiiSdQVVWFTZs2YcyYMV3XhrBbNN1OhsvlImVlZWTSpEkkIiKCvPXWW8RqtXaaddRms5Gqqiry/vvvk8GDB5OgoCAya9YskpeXR1wul0ee63Q6SUtLCykqKiJbt24lkyZNIqGhocTPz4/06dOHJCUlkYcffph89NFHpKioiBiNRuJwOH732RRFkbq6OpKfn08aGxuvS4PD4SBGo5GUlZWRrVu3kkcffZQMHTqUREREEH9/fxIcHEwmTZpEPvnkE1JUVERMJlOXGd7cbjfR6XTkgQceIBqNhmzcuJE0NTV1aEyaponL5SKvvvoq6dOnD7nnnntIUVFRlxnz/pDM2dLSQrZu3Uo0Gg2ZO3cuMRgMnTqh+fn55NFHHyV+fn4kJiaGvP7666SqqqrDpv3W0Ol0ZOPGjWTMmDFEqVQSsVhMhg0bRp5//nly+PBhUlpaSiwWC3E6ncTtdhOapq+7KVgsFvLee++RQYMGkW+++ea6NDBjUhRFnE4nsVqtpKysjPzwww9k9erVZMSIEUQulxOFQkHGjh1LPvroI1JfX++pKbgu3G43OXLkCImPjyexsbHkyJEjHhm3rKyMzJ49mygUCrJt2zZit9s9Mu718IdkzoKCAjJkyBCSmJhIMjIyOqVeDE3TxG63kyNHjpCxY8cSX19fctttt5F9+/YRg8HgEca02+2ktraWpKWlkbFjx5KgoCDSt29fMm3aNPLFF1+QoqIiUldXR2w2G8uQ7YHJZCJr164lcrmcbNu2rd30MTWPbDYbqa+vJ0VFRWTnzp1k8uTJJDY2loSHh5PU1FTy/fffk6amJo9uVteCXq8nK1euJL6+vmTu3LnEaDR2OMTPZrOR3NxcEhYWRlJTU0lRUZGHqP19/KEihGiahslkwnvvvYfMzEw89NBDuOOOO+Dt7e1RRZ6iKDQ2NuLQoUNYtWoVysrKkJycjJUrV2L48OEdMvyQ/xWPNhgMyM7OxocffogPP/wQLpcLiYmJePzxx7Fw4UIMGTIEPj4+kEqlN11XyOVy4ezZszh9+jQmT57cbmtk6+wTLy8vqFQqxMTEYOLEiQgLC4PRaERxcTHS09NhNpshkUggkUg61borEAgglUpx4MABGAwGxMXFdVj3ZAL0CSE4duwYLBYLRo0a1WlVG1h0yRbQRWBOsuTkZBITE0MKCgo8vlvTNE1aWlrIunXriI+PD/H39ycvvPACG6HS0ROaoijS2NhIli5dSiIiIohAICBz584lx48fJxaL5aZOyGvBZrORXbt2kRkzZpD09HSPjEnI/+tqTU1NZP/+/WTq1KlEoVCQ/v37k5UrV5Lm5maPPetqz25qaiL3338/8ff3J48//vgN6dPXg8vlIhUVFeT2228n0dHRJD09vdOjqv5QQQgOhwN79uyB2WzGokWLEBYW5tE0LIqiYLVasXnzZmzZsgVqtRrPPPMM7rrrLo/kgjY0NCAnJwcvvfQSKioqoNFosGzZMkyZMoV1f3hSAhAKhZg8eTJGjRrVxrpqNptx+vRpHDt2DGfOnEFjYyM4HA5bxItJCHe5XIiNjcXkyZMREBDAXudwOODz+VAoFBg1ahRiY2Px+eefY8eOHXj//feRnZ2NF198Ef369fN4bDGHw4FEIsHs2bNx7tw5nDp1CiaTCUqlskPP4fF4CAgIwMyZM1mrcFxcXOcGZHQq63chbDYbOXv2LImOjiazZ88mdXV1Hj81a2tryVtvvUUiIyPJsGHDyBdffEGMRmOHTzK73U7Ky8vJpk2byMiRI0lAQACZPXs2OXToELHb7Z1mzHK5XKSgoIDs3r2blJWVsdeZmNvS0lJyxx13EC6XS6RSKXn55ZdJbm4uKSwsJLt27SJTpkwhvr6+5L777iNffvklaWxsvKp+x4Tbff311+Suu+4ifn5+ZNy4cWT79u2ktrbW4yl7breb1NXVkbvvvpuoVCqyd+9ej51ypaWl5K677iLh4eHk6NGjxOFweGTcq+EPw5xVVVXkoYceIsHBweTzzz/3uAGIoiiyefNmolAoSGJiItm9e7fHCisXFhaS6dOnE7VaTUJDQ8m7775LqqurOz0w3mQykfXr1xOVSkU+++yz3/w/RVFk8eLFhMvlEo1GQ86cOcPSRNM0OXPmDCt6R0VFkW3btv1ud2m3203KysrIk08+SbRaLSt2lpeXe/S9aJomTqeTvPHGG0QikZAFCxaQ6upqj4xtt9vJp59+Svh8PnnqqadIXV2dR8a9Gv4w+Zy5ubnIyMjAmDFjkJiY6FFRiaZpZGRkYMeOHZBIJFi6dCnGjx/f4XIZhBCcPHkSixcvxoEDBzBw4EBs3LgRs2bNgo+PT5dEozANgVs3QWLAFMT69TXmz4iICCxcuBAymQw1NTXYuXMnjEbjNZ/F5XIREBCAZcuWYcOGDYiMjMSuXbvw7LPPIicn56o03AyYFLDBgwcjNDQUGRkZaGxs9MjYAoEAI0eORHJyMvbt24cLFy54ZNyr4ZZnTpqmUVtbi++++w52ux3jxo1DcHCwx8Z3u90wm8349NNPUVFRgYULF3bYAkzTNIxGI77//ns8++yzOHXqFMaOHYuXXnoJkyZNglKp7JIiU0wdHR8fn5vSnWQyGQYPHgyhUAiHw4GamhqYzeZrfr918vTUqVPx/PPPo3///sjMzMTatWuRk5Pzu/e3B1wuF4GBgUhKSkJjYyN++uknj42rUqkwbdo0WCwWfPzxxzAajR7bWNo8y+MjdjFcLheysrJw8uRJiEQi3H777R2Kqfw1HA4H0tPT8cMPP2DUqFFYvHhxh40LTqcTe/fuxcKFC3H69GmkpKTg3XffZWvXdOTNk3cAACAASURBVBUEAgEmTJiA1atXIzExsd33MycUMxftqeyuUCgwduxYfPTRRxg0aBD27duHRx55BKdPn24TfN8R+Pv7Y8SIEaBpGjk5OR4bVyaTITU1FUqlEqdPn8apU6fgdDo9MnZr3PLWWrfbje+++w42mw3z58/3uDjY0NCA9957DwEBAbjvvvsglUo75NuiaRr79+/HypUr0dzcjHvvvRfPP/88/Pz8ujyzg8fjISoqClqt9qZiYVtaWnDs2DHYbDYolUqMHj0aGo3md+9xOp3Q6/Vsl7PCwkI2QL+0tBSrV68GTdMYP358h+dDKBSib9++EAgEbHZOR32ewBW/Z3R0NIYOHYqDBw/iyy+/xMCBAz1uub2lmdNmsyE/Px9HjhxBYGAgZsyYwXZs9gQIIbh48SLOnTuHsWPHYuDAgR1yzdjtdvz444946aWXYDAY8MADD+Dpp59GdHR0l1feA65sbJmZmThy5AhmzJiBpKSk695D0zTcbjdaWlqQkZGBPXv2QK1WY8KECXjkkUd+d4E2NDTg6NGj2LdvH4qLi1FeXo7GxkY4nU5wOBwolUrk5+fjlVdegbe3N+Lj4ztUx1cgECAmJgZqtRp6vR75+fkIDAzsMHMy6sB9992HH3/8EceOHUN1dTV8fHw8mid8S4u1TU1N2LhxIxobGzFmzBiP7Iqt4XK5cO7cOTQ1NWHo0KEdSuKlKApFRUVYvnw5CgsLMXr0aLz88svdxpjAlVMsJycH77zzDi5evPi7322dM1pUVIQNGzZg+fLlcLlcWLduHdavX4/+/ftftVwl+V+nr/T0dCxduhTbtm3D8ePH2d6gTMX38ePHY+TIkThz5gzmz5+PS5cudUiX43K5LJM3NzejsLAQbrf7psdrDQ6Hg6SkJCQlJaGyshI//fQTHA6HR8ZmcEszZ3l5OU6dOoXQ0FCMGDECAoHAo6JhWVkZioqKoFKpkJSU1CEjTXFxMdatW4eLFy8iNTUVa9eu7fHt81rD4XBg586d2LhxIx555BF88skn0Gq12Lp1K+64447frRJgMpnw2WefYfny5aiurgZN07/5jlgsxqRJk/D888/j/vvvR1FREdavX4/8/PwO0c3j8ViJp6am5qrPvhlwOBzI5XLccccdAIA9e/agvr7eI2MzuDVWxlVAURRyc3NhNBoRHx+PuLg4jy/06upqnDt3DjweD6GhoTc1PtN24IMPPsDRo0dx++2344UXXkBcXFyXFbG+Fng8HhQKBaKjo6+rc4rFYvzlL3/BzJkzMX36dABASUkJ9u3bB0LINSUWs9mMjIwMfPrpp6yO++uKdhwOB2KxGCkpKejfvz8WL16MsWPH4syZM9i6dSuMRuNNn3g8Ho+t2FdbW+sx5gSu6LQDBw5EdHQ08vPzryt9tBe3JHMSQmA0GpGfnw+Hw4GRI0d2SOS8FmpqaqDX69kf92YYyeFw4JtvvkFaWhp8fHywcuVKxMfHd381cQAikQiPPfYY0tPTMXHixN/9LofDgbe3N0JCQvDYY49h3LhxaG5uxnvvvYdTp07B5XJd9b66ujoUFhZi3rx52L59O1577TW2HwojznM4HPj5+SE4OBhSqRQxMTF488034evriy+//JI1+N0MeDweEhIS0LdvXzQ1Nf2mVEtHwOFw4Ovri9tvvx12ux1Hjhzx6Pi3JHNSFIXz58/j559/hkAg6DQXRElJCXg8HlJSUm6q9L/b7UZhYSE2b94MkUiEf/7zn+jXr1+PaZRD0zQMBgMuXbqElpaWG7qHy+VCLpfjqaeeQkpKChoaGvDqq6/i3LlzV/1+cHAw5s+fj8mTJ6OiogIrV65EY2MjWzaFacsQGRnJ3sN0AluwYAHUajVWr16N3Nzcm9I/ORwOW7ng559/Rn19vcf0TuCKS2jkyJEQCATIzs5GVVWVx8a/ZZnz559/hl6vx/Dhw9kf2dNgmHP48OE3xZz19fXYvHkzysvLMWXKFNx7773dXkS6NVwuFw4dOoQVK1Zck7muBkaPe/LJJxEcHIxz585h48aN0Ov1vzlBGTtAVlYWXn31VRQVFWH48OGYM2cO2/V6wIABmD17NvsbcrlciEQiTJo0CXfffTeqq6uxdetWVFRUtPsdmbH69u0Ls9mMzMxMWK3Wdo9zLYhEIgwePJi1CGdlZXnM53nLMSf5X3W7H3/8EVwuFw8//HCnVNMjhKCkpAQKhQJRUVHtOu0IIXC73di/fz92796NhIQE/P3vf4evr2+PMgBRFIXq6mpkZWWhrq6uXfeKRCKMHDkSixcvhlAoxJEjR7B161aYzeY2Yp3dbkdOTg7+/e9/o6CgAP369cP777+P8PBwNDQ0QKvVYsWKFZg8efJvRP2AgAAsWLAACQkJOHDgAA4dOgSKotolNnI4HJY5BQIBDhw48Lshhu2FQCBAWFgY4uPj0dLSgszMzJsWwX+NnrNSbhAURbEdlAMCAjBq1CiPi4mM6b+urg5qtbrdqVputxu//PILPv30U8jlcjzxxBO3ZE8UQgjbL4RxpbSGXC7HtGnTMGbMGNhsNnzyySfIyspi76EoChkZGViyZAkqKiowcuRIvPbaawgNDUVLSwuCg4Px8ccfIzU19aqSD4fDgY+PD9atWwdfX198/PHHuHz58jX122uBw+GgT58+6Nu3L7Kzs1FWVnaTM3J18Hg83HvvvZDL5cjLy4PFYvHIuLccc1qtVqSnp6O5uRkJCQlQq9UeN6643W7o9XrY7XZ4eXlBIBC0i7Hsdjt27tyJ+vp6TJ06FSkpKd1eiPlqYJz0U6dORVhYGHvd4XCgsbERJSUlKCwsZOvbnj9/HlVVVTCZTHC73eDz+fDz88O///1v9OnTB2VlZVizZg3S0tJw6dIlfP/991ixYgUuXbqEESNGYNWqVRgyZAiEQiE0Gg2ee+45jB49+nclH7FYjCFDhmDKlCkwmUx45513burkCw0NRWJiIsxmM7KysuB2uz1nuOFykZSUBH9/fxQVFbGVCTuK7jcZthMWiwVHjhwBl8tFVFRUp4i0LpcLv/zyC1wuF+RyOYRC4Q0/w+124/Lly9izZw/8/PywaNEiyOXyHiXOMhAIBJgyZQrGjx/fJh7ZZDIhMzMTx44dQ3NzM9u38/vvv4fJZMKYMWOQkJDANscdNmwYVq9ejRUrVsBsNmPjxo3w9vZGfn4+7HY7BgwYgLfeeguxsbEQCoWgaRr33HPPDfXA5HK58PLywqxZs5CTk4OvvvoKkydPxtixY9u1KatUKiQnJ2Pbtm3IycmBwWCAr6+vR9YOh8OBSqXCkCFDkJ2djezs7HarQldFpyWjdRIKCgpIYmIiSUhIuKGKcTeDhoYGsmrVKuLj40OeeOKJdpUGqa6uJkuXLiVqtZp8+OGHnVJczFNwOBzk1KlT5M033yTnz59nr1MURRwOBzGZTKSpqYkYDAZiMBhIc3MzW+Gv9TvRNE2sVisxGAykrq6O7Ny5k8TGxhKhUEhSU1PJqVOniN1u/8097ZkXm81GduzYQYRCIVm8eDGpqalp17u63W5y/vx54ufnR+Li4siXX37p0Sp6LpeLbN++nUgkEjJjxgxSWVnZ4TF73nZ+HVRWVqKxsRHBwcEIDw/vlGc4HA7k5ORALBYjJCSkTebF9VBYWIi0tDQMGzYMw4cP7/ZAg9+D2+3GiRMn8NZbb7VxoDMt92QyGZRKJTQaDVso+mpiPhNEIJVKkZ2djTVr1qC6uhqjR4/GK6+8gkGDBv1G+mhvLixjgBo+fDgOHz6MS5cutetduVwugoKCcPfdd8NiseDQoUMedanweDxEREQgPDwceXl5HokWuqWYk6ZplJeXw2KxIDw8HEFBQZ3yHLPZjJKSEiiVyja62PVoMxqN+Oyzz9DS0oLJkycjJCSkxzImcIVmm82Gurq6DlkYCSGw2Ww4ffo0nnvuOZSXl2PQoEHYsGED25y4o/PABMb/9a9/hdFoxHvvvQez2XzDET9MbaHHH38cKpUKhw8fRmVlpcfcHhwOB1qtFgkJCbBare1yTV0LtwxzMgugrKwMNpsN/fr1uynf442goaEBJpMJWq0Wffr0uaF7XC4XDh8+jOPHj0MmkyE5OdmjeaU9GYQQHD9+HE888QQuXryIpKQkvPHGG+jXr59HjXVeXl4YNWoUAgICcPLkSRw+fLhdm4pAIEB0dDRGjx4Ng8GAN954Aw0NDR6jT61WIzExEW632yPJ3bcUc9bU1KC4uBgAEB8f32nt4g0GA0wmEzQaDUJDQ2/oHpfLhZMnT6KlpQVJSUmIiorqtmyTG4VQKERqairWr1+PIUOGtPt+QgicTicOHjyIRYsWoaSkBKNGjcLbb7+NgQMHeuTEbA0ej4eQkBAkJCSAoqh2h/Ux4ndqaipCQ0Nx6NAhFBYWeow+iUSCAQMGQCAQoKioCDU1NR3LqvEYZZ0MQgiqq6tRVlYGtVqN8PDwTolPpWka9fX1sFqtCA8Ph1wuv6H7GFFGKBTi/vvv93gZy84An89H//79MX369BuWEFrDarUiKysLK1euhE6nw5AhQ9g0uPa6n24ETLTP6NGj2dbz7QmeYCo3DBw4EMOGDUNzczPS09NhtVo94lYRCARsucz6+noUFxd3SK+9pZiztrYWjY2NSE5O7rQwOJvNhpqaGjidzhsOC2T0zZKSEvTp0wcTJkzotFPdk7Db7dizZw8effRRHD9+vF330jSNkydPYsGCBfj5558xePBgvP3226yLpbPA4XAwZswY9OnTB5WVlaitrW33GP7+/pg0aRIoikJmZiYuXLjgkRpAfD4fWq0WWq0WJpMJOp3uz8Oc1dXVIIR0alYH43wnhCAyMvKGntPS0oIDBw6gpaWlw+0YuhKMge3kyZM3fAKR/0VPHThwAE8++STKy8sxduxYvPPOO2yIXGdKDBwOBxqNBrfddhtaWlqQm5t7w0H7DIRCIUaPHo2YmBiUlpbizJkzHksl4/F4iI6Ohsvl6nCKWs9fQa2g0+nA4/HYXMjOACOOKBSKG87hbG5uxp49eyCVSpGcnNyj3Se/BvlfHPCNinVWqxUnTpzA6tWrUVlZieTkZKxatarTRNmrQSQSYdy4cfDy8kJmZiaampradT+Px4NcLseCBQtACMGhQ4fgcrk8ItpyuVzExsaCw+Ggurr6z6FzAleSn/l8PmJiYjqNOauqqlBeXo6kpCTI5fIbWmyXL19Gfn4+Bg4ciIiIiFuGMdsLphP23LlzkZeXh8TERLz//vsYNGhQl6bBMYahxMRE/PTTTygvL2/3GCKRCHfccQeCgoJw7tw5NDQ0eES05XA4iImJgUAggF6v/3MwJyEEOp0OMpmsU8XGvLw8EEJw11133XBxqfPnz8PlcmHIkCGdkvTdWRCLxfjb3/6G9PR0ttzGtUBRFPbu3YulS5eipqYGEyZMwKZNmxAZGdkt+alyuRypqalwuVw4depUu+/n8Xjw8fHB4MGDYTab8dVXX8FkMnWYLi6Xy0oRHrXWulwuNDY24syZM8jIyMCRI0dw5swZlJWVoaamBjU1NcjLy7tmUK/D4YDJZILT6fSYDO90OmE0GqHX61FeXg5vb+9OMQYx4t2ZM2fYkhnXS+AmhMBsNuPnn38Gl8vFgAEDurTdekfBzOH1ai9ZLBZkZmbi5ZdfxuXLlzFs2DCsWLECffv27TYRXiKRIDk5GWKxGMePH4fD4WjXmuNyuZBIJBg0aBDkcjn27t2L5ubmDtPF6MQqlQp6vd5zOqfFYsEHH3yAGTNmICsrCyaTCdnZ2Zg5cyYWLFiAZ5555nd3mJycHHzyySe4ePGiRyqR0TSNkpIS7NixAwsXLoRer4dSqYREIvH4yUlRFPR6PYqKiuDr64vg4ODris40TaOwsBAlJSUQCoWIjIzs8b7N1mCyZ+6//34cO3bsqt8hhOD06dOYPXs2cnJyMHDgQGzdurXDBc86CqZaglKpRGlpKUpLS9t9SnE4HMTHxyMiIgKXL19GVVVVh+liqtr7+/tDr9d3yFrLB67EWJpMJqxduxZHjx7F0qVLMXXqVMhkMlAUhREjRmDt2rU4cOAA5syZc83BTp8+jddffx0bN26ERqNBYGAgG5ep1Wrh4+MDpVLJ1pZlTiuHw8GeuvX19aivr4dOp0NFRQUaGxtht9vhdDqhVCoRERHRKSenxWLBt99+C6PRiCFDhkClUl13A6AoCiUlJTAYDPDx8UFQUNAtYaVlwJz81wrfo2ka33//PVatWgWDwYBJkybhxRdfRHBwcLe/J5fLhZ+fH3x8fPDLL78gPz8foaGh7d4wQkJCEBISgvz8fJSXl2P06NEdpk0kEiEoKAh2ux0VFRXw9fW9KdcaH7gijh45cgRpaWkICAhAamoqfHx82AHlcjnmzp2LCxcusEx1NfTv3x9Tp05FeXk5ampqcOHCBTidTrjdbjaDXS6XX5M5mcJPAoEAQqEQarUa/fr1g7+/P0JCQqDRaJCUlNQpDn6TyYQDBw6Ax+MhNjb2hlLRaJqGTqeDxWLBkCFDPFrQuqvA5XKv2kbBYrHg7NmzWLduHUpKSjB8+HA8++yzGDBgQI+QDhix1N/fHwUFBSgqKrqpU0qhUKBfv35IS0vD5cuX4XA4OhQWyvQm9fHxAU3TqKioQEJCws0zp9FoxOHDh9HU1IQ+ffpAqVS2+QH4fD4GDx6MO++883eThidMmIBx48bB6XTC5XLB4XCgsrISxcXFKCwsRGFhIUpLS9kqaFwul8168PHxQXBwMKKiohATE4OwsDAoFAoIBALw+fxO122qqqpQUFDAbgA38iwmpJCiKAwcOLBHVNRrD5imPBEREWwRLODKe509exb33nsvjEYjRowYgS+//BIajaZHMCYDptNZenr6TVVIAK74POPj40FRFCoqKtDU1AQ/P78ON9pl4qpbWlpuWrTlA1d0j/r6erYEyIULF9goHAbe3t6YOnUqMjMzrzkYEx4lFoshEokglUqhUCgQExODCRMmwOVyweVysboBkzbElElkkneFQiH4fH6bTtGdyZh2ux0XLlyAXq/HxIkTMXjw4Bu6j6leJxKJbknmFIvFmDNnDiZPngyVSgXgCmN+++23WLNmDUwmE+6++26sWLECGo2m20XZX4PD4SAyMhJisRj19fU3ZedgikMDV9SUjhoyORwO266BEAKLxXLTY/KBKz+Sn58f+Hw+ampqsHnzZgiFQvTr14+1PopEIiQlJcFkMl332G+dq8fj8Tote8RTqK+vx7Fjx+B0OjFx4sTrNuNhQAhBQ0MDO1c96VS5ETAGt/z8fAwfPhwcDgenT5/Gyy+/jKKiIowcORLPPvssEhMTe+S7MSenWCxGU1MTW7uoI/BUIAKz5jvCnFzgSkuzlJQUKBQKNDY2YufOnZgzZw6OHj3K6oqMjH/nnXe2EYH+CLh48SIOHjwIhUKB22+//Yb1A/K/4tZeXl7w9/fvkQv492C32/H9999j/vz5OH78OHJycnDvvfciLy8P/fv3x7fffoukpKQeKxFwOBwEBARAJBLBYrF4JDfTU2VLmJOzPTmnvwYXuOIzuueeezBv3jyEhISwcaxPPPEE5s2b16ZJy61m8LgR7N+/H1wuF3PnzoVGo2nXOzLt627VeSGEgKZpHDhwAEuWLIHFYsFdd92FN998EzKZrMeJsq3BJFBzuVy43e6bYgKmmBshBFKp1COF2JiO4AKBoONiLZ/Ph7e3N/76178iODgYn3zyCXJzc1FdXY0dO3ZAp9PhoYcewrhx46DVam+JjIsbAVP+8ujRo5BKpbjzzjvb1XKOCQLviZX1bgSM+kEIwb59+wAAKSkpeO655zBo0KBbQhJgDIY3y5xOpxP5+fng8/kICgqCVCr1yEbL5/MhFAphsVhuOkqojbwSEhKCBx98ECNHjsSCBQuQnZ0Nm82GH374Abm5uZg1axaWLl0KtVrNyuYMERRFwel0stdFIhH4fD4cDgdrrWKOew6HA7vdzk4mMwZN06zewDhzeTwea0gC0EbZdjqd7IszY7jd7jZBzIxxiXHpMJBIJLDZbPjuu+9QV1fHWogFAgHcbncbOphd0OVysaITl8sFTdNwuVyQSqXsjyAUCiEWi+F2u9vMx7XoEIvF4HK5sNlsbfQdLy+vNvPBvKNIJGpDB1M0mcfjtZlrxjDH/C7MXDMGN5vNBrvdDpVKBR6PB5vNhuTkZGzZsgUqlQp2u509mSiKaiM5MXPNWOWZ+WBcSQ6Ho83vIhKJrjofAoEAdru9zeJl5qN1VXZmbNKqji7zjsxaczqdMJvNsFqtEAqF4HK5behgbB80TbeZj9raWhQWFkIikcDX15d9J5FIBC6X22adttYlW/uFW6895ndxuVwsc1qtVpjNZpYO5nBrHdXE/C5t6iyRX2nANE2DoijU19dj3759+O6775CRkQGr1QqJRIJhw4ZBo9GwUULjxo3DnDlzcPbsWbZ+DgDMnz8ft912Gz766COcPHkSTqcTKpUKTz/9NORyOdatW4fq6moIBAIMGTIE8+bNY9vkURQFpVKJBx98EElJSdi7dy/S0tIAXKk/umzZMpjNZmzfvp1tEZeSkoL58+fjxIkT2L17N1t+4pFHHsHYsWOxZcsWZGVlsYvs9ddfB0VRmDdvHvLy8tjiT8888wxKSkrw5ptvwm63Qy6XY8qUKZg8eTK++eYbfPHFFwCuVCN/4oknsGDBAuh0OvTt2xdcLheDBw/G0qVLcerUKezcuZPNN3zggQdw991344MPPsCZM2dYOpiu1i+99BLq6+tBCIGXlxfefPNNVFRUYP369XC73fDy8sKIESMwd+5c7N27Fzt27AAA+Pr64rHHHkNMTAzeeust5ObmAgBiYmLw0ksv4cKFC3j//feh1+sBAPfccw8eeOABvPjiiygqKkJRURFKS0uRkpKCRx55BF9//TUoimJ9dWvWrEF+fj42bdoE4IrPe9KkSZgyZQq2b9+OgwcPsvOxaNEiqFQqvPLKKygpKQEADBo0CM8++yxOnDiB7du3o6GhAVwuFzNnzsTdd9+NTZs24dy5c3A6nRCJRFi6dClCQ0Mxf/58lg5/f38888wzqKqqwvr16wH8f8mSqVOn4m9/+xtOnjyJIUOGIC4uDg8//DDi4uKwYcMGFBQUAACSkpLw97//HXV1dfjPf/7DpshptVpUVFQgJycHcXFx8PX1hUwmw7/+9S9ER0ezieRMYep//etfsNvtePrpp9vQ8cADD+DYsWPYvn07gCsuFJ1Oh/j4eAQHB6OyspKdj4cffhgUReG1115jf5f7778fM2bMaOPDZyOEbDYbJBIJ68IICAjAjBkzMHz4cKSlpeHdd99FfX09MjIyoFarIZfLwePxEB8fz+4CxcXFLNNaLBZwOBwYDAaUlJTA5XLBx8cHFEWBoihUVVWhrKyMFSc4HA6sVisbhqVQKGAymcDhcFBfX4/S0lJ2R2I2kIqKCvZ6REQEewKVlpayzMmM0dDQgJKSEnZnoygK5eXl+OWXX9ioJb1eDz6fD7PZjLKyMlitVkilUjQ3N4PL5aK2tpZ9ntlsZk8Uh8PB9lVhXA42mw0lJSXsImAWJTMfrXdYQggqKyuh0+kAXDHQ8Xg8dj7cbjckEgmioqLA5XJRV1fH0tHS0sKeMiUlJex1Zs+12+0oKipiq8HV1NSAy+WiuroapaWlsFqt4HA4SEhIQGJiIjZt2gSn08k+n8fjwWg0suNKpVI0NTWBy+WiqqqqzXw4HA4QQnDp0iW2r4m3tzc4HA7MZjOKi4vZew0GAzgcDmpra9n1IRKJYLfbwePxUFJSApqmWZGVkbaY50kkEsTFxYHD4cDlcsHtdqOyshICgQA2mw1cLpcN62M2MaYrd3FxMes6vHjxIiiKgq+vLxoaGmA2m6FQKGC1WsHlclFZWclWiOfz+aBpGjRNs+OKxWL069cPXC4XTU1N7HXGQOV2u9vMk1arZTuRFRcXs+vDYDDg1+AQQojRaMSxY8eQkpLyGzcC4y545ZVX8Pbbb8PpdOIvf/kLVq5cCblcDoVCAZVKBavViubmZlaM0Gg0kEqlaGxsZMtA8Hg8aLVacLlc1NfXw+VysaKTWq2G0+lkTxoej8fG0ZpMJvZEFgqF0Gq1oCgKzc3NrJgjlUqhVqthsVja9HNUq9UsHTabjRUjvLy88MEHH2DNmjVYt24d7rnnHnh5eUGr1cLpdMJgMLBWaoVCAblcDqPRyAZHCwQCiMViTJgwATKZDP/9738hEokgk8ng4+MDq9WKlpYWVuxTKpWQy+Vt5oNZNAKBALW1tW0s44GBgaxOzFzz8vKCWq2GyWRicxgFAgFUKhVEIhEaGhpYRmXcY3a7vU0FcoVCAaVSCb1ej+bmZnz88cd45513sHnzZsyaNQs1NTUghLDiKzMGs3h4PB5kMhkUCgVaWlrY6usCgQA+Pj7g8XhtfI7MnFosFjQ3N7OMxsyHwWCA3W5nn6nVaiEQCKDT6dhrAoEAWq2WnQ/g/4tNczgcPPDAAygrK8N//vMfDBw4kJ2P+vp6dn0wc8f0S7Xb7TAajVi2bBlyc3OxevVqjBkzhjWCaTQadsNm1pJQKGQjf2pqalg6pFIpvL29YTab2fWRnp6O5cuXY9SoUVi+fDnrR5ZIJFCpVCCEwGAwsL+Lt7c3lEplGwMcG4SQm5uLgQMH/oY5mb6MM2bMwOnTp5GdnQ21Ws3GuDI1XWUyGaRSKbvomAACtVrNEtb6ur+/P/tdxnErkUgQEhLCXmM+SqWS7ZzMfJfP58PX1/c3z5PL5ZDJZL+5rtFo2uh0BQUF+PrrrxEWFoaJEyciLCwMXC6XHZspu9maDm9vb9ZhzZwGjG4SFBQEsVjMWm6lUim8vLyuSodarf7NfAQEBLSZdyYoIzg4uM1vwWwWjDuLuQb8/67MjMvMmkvHIAAAIABJREFUaUBAwG/o8PPzYxcVE8InFArbPI+hQyaTsUav1vOhUqlYP3hrOvz9/X9Dx7Xmw8fHp83vwuiRV3tvPp/Prg8GRqMRTqcTEokEgYGBCAgIYOnz8/NrQwcT8BIQEACLxYLi4mKUlZUhLCwM9913H6t/t6aj9dwxdBBC2tDBXG+9Pry9veFyuaBQKODr6wt/f//fjPHr3+XXlnE+cEXEq62txalTp+Dj4/MbP6ZAIICfnx/Cw8Nx6dIlhIaGQiqV3lAEz7Usfte6fjWfWusfvvW1q+FG6SgrK4Ner8e4ceOgUql+EzB9I3RwuVwIBAJQFMUyE/P/7Z2Pa/kSb3Q+rnWdWZBXG1ckErHJBAqFgj0tO4OOa7lkOrIOGGs507dFIBC0Ge9a88HEdG/ZsgU2mw3Tpk1jVZsboe9G3puhTSaTsRblX3/3euAzAzHExsTEIC4ujrWUAld00rq6OlRWViIyMhLDhg27YTM740djQqOYT+vd6NcfZhdpT6X19qKoqAhcLhdDhgzpUH1ZkUjUobbo3QmmUuCIESM6rXp+Z4IJj6Mo6ro5qa1BURRKS0uxf/9+BAUF4bbbbvOo24jxJLjd7g75ituwc3l5OZ599llMmDAB99xzDyIjI0EIQW5uLnbs2AFCCJ5//vkbTqthKoozpT+YbJWmpiZ2QUskEigUClYkUCgUUKvV6NOnD6KjozutxGRJSQlb8uRm/bYcDgcKhQJ1dXWoq6uDl5fXLeEbZNBa378VfdeEEOj1ejgcDqhUqht+B4vFgsOHD4OiKIwcORLJycke/d0YFxij7t3s2HzgirI8ZswYzJkzB+Xl5cjNzcWbb74JpVIJiqLQ1NSEwYMHY86cOejbt+81Txq9Xo/S0lLk5ubiwoULqK6uRkNDA+vrsVqtrNGjtZ7x61OTCZpXKpUICQlBbGws+vXrh5iYGGi1Wvj5+d3Uy7aG0WgEn8+Hl5fXTe9sjA5ZUPB/7Z15WFN3use/BEggYQmBsAcEwYVNoOKCKK51q1rHpWqrttrW2tb2dlqtXWw7U7V2cW4747RVe+d2s0696rg7Vq0oCgoIKKAgu+w7gewnOe/9w56M1g0hIYD5PA/P42PgnF8g73l/v3f5vnnIy8u77TzU09HpdPj555/x/fffY926dZg6daqll/RAEBFKSkqM+dqOFoMUFxfjzJkzcHBwwMiRI+Hh4WGySihup8gForrsObmAj52dHcaMGYOnnnoKarXamDR2dHTsUK/ijh07sHHjRuM2QygUwsHBAQ4ODhCLxfD394eXlxckEglcXV1hZ2dnjGq2trYa0wIMw0ClUqGyshIFBQU4cOAA9Ho9AgIC8N5772HhwoWderN34uYi/QeFx+MZo7uXL1/GxIkTTbau7oCLXGZnZ98xlN/Tod+mj2u12g43NBMRrly5gtzcXPj4+CAuLs7kJYo3e04u5dgZ7ID/VMFwcNsdR0dHYzi7Ix9gHx8fjB49GvHx8YiMjIRUKjUap6OjIxwcHIyNvTcfnLmnDXf25YyTS4tcvXoVJ0+eRH5+vjFdc3MwylJwUWcej4fLly+bZGCqlY7DGafBYEBQUNB9VRC4iq78/HwoFAosXrz4tii5KTAYDMb8uru7e6cbB+76U53po5w2bRoSEhKMIlymOMewLIshQ4YgKCgIy5cvx+XLl6FWq7s8NFcsFoNhGLS3t3e69pFLoYhEIuTn5xt3GpZ+aHQUe3t7+Pr6YuzYsb1KNRC48blQqVSor6+Hvb19h4bVcsOw8vLywOfzMWfOnA6P2+goXJS2rq4OPB6vQw+Nu2FSfy4WixEQEABXV1eTBRi4HFlUVBRsbGxQU1MDlUrV5abY4OBgowZQZ1uNbG1tERISAqlUiubmZlRUVJhMdbA74PP5WLx4MXbv3o3ExERLL+eBYFkWdXV1aGxshFAoRGRk5H09lMFgQE1NDUpKShAcHIyBAwfeV2HxQeEitXV1dXBycuqS5+y5/UA3wVULSSQStLS03FYk3hn69+8PlmVx6dKlTs+m5PF4GDx4MEJDQ6HT6YxbrN6CXq/HlStXsGfPHmOJWm+BK9draWlBaGhoh/RzGYbByZMnoVAoEBsba7Ydjk6nQ319Pby8vLp0nu0Vxgnc2F77+flBLpd3qUeOIygoCEKhEBkZGbd0QDzomgQCASIjI42Gbgrt0+6CYRicOHEC77//vknmSXYnSqUSKSkp0Gq1SEhI6FBPrU6nw9GjR421xOboVSUiNDc3Qy6Xw8vLq0spml5lnP7+/tBoNKiqquqyh3J2dsaAAQNw7dq1Lov/RkVFwcHBAdnZ2aiuru7SuroTLg9dW1vb6QeUJeAUBn799Vdjp9T9YFkWra2tyMrKgru7u9nmp3LSLwaD4eHxnMCNekuDwYArV650uSJHLBYjOjoaBoPhnir2HUEmkyE8PBwZGRnGCWW9id4SwOLgJCfT0tIQERHRofwy142i1WoRGBhotmFYXLcJwzAPn+dkWRZ5eXldNk6RSISIiAjw+XwkJyejvb2900YlkUgwb948GAwGpKWlmWxilbnhBtGuW7cO0dHRll5Oh9HpdDh+/DhYlsXYsWM7JMjGMIyxx9Tf3x9SqdQsDyUuvcOy7MPlOb29vSEUCpGZmdllAxAIBBg0aBCCgoKQn5+PS5cudfp6Tk5OGDduHMRiMVJSUtDc3NwrAkO2trYYNmwYli9fjpCQEEsvp0NwWsHJyclwdXVFVFRUhwTnlEolSkpKYGtrawwemdo4uUhtfn4+BAIBfHx8Hg7PyTWA+/r6oqCgwNhv2RX8/f0xYcIENDY24vDhw52+nq2tLdzc3BASEoKqqiqcPHmyVxQkaLVa7N+/Hy+88AJSU1MtvZwOQURITk7G9evXERAQAG9v7w4ZWX19PYqKimBnZ4fg4GCzrI1L1VRWVsLV1dU4bayz9Brj5KK1ISEhxg72rkohOjs749lnn4WHhwcyMzNRUlLS6Ws6OjoiKioKGo0G//d//welUtnjt7Ysy6K0tBRJSUlGuYyeDBfAOnv2LNRqNWJiYiCVSjv0s3K5HHV1dXfsWTUVOp0OBQUF0Gq18PHxQUhISJfOtb3KON3c3BAUFAQ7Ozvk5eV12TgFAgEiIiLwxBNPoKKiAjt37uz02dPe3h6JiYmQSCTIyspCQUFBj28jIyIYDIbbRLZ6KgzDoKysDFlZWbCzs8Pjjz/e4WJ3hUKBlpYWeHh4dKlF8F5oNBqj7MnAgQNvUzZ4UHqNcQI3to9co/fNekVdZdasWfDz88OGDRuQlZXVqQ+qQCDA9OnTMX78eLS3t+PChQu9Ij3BdQL1hoitWq1GUlISampqMH78eEyZMqXDUqZcg4VMJjNbe1xrayvy8vJgb2+PqKioLl+vVxkncCNt4ezsbBQIM9U1Fy1aBKFQiHfeeQenTp3qlPfk8XhYuHAh/Pz8sHv3bhQWFppkfebCwcEBCxYswJ49ezBu3DhLL+eecOV627Ztg7+/P1asWNFhr0RExpZFmUxmtrmijY2NyMnJMU4u6yq9zjh9fHzg7++PqqoqlJWVmeRc5+LigunTp2POnDmora3F9u3bce3atU6V9YWEhGDJkiUoKCjAyZMnbxEV62lwRwWZTGa2rZ6pUKlUOHr0KAoLCzF9+vQHii5zxmkwGIwCYqZGr9ejuroaZWVliImJ6fC8nXvR64zTyckJ8fHxaGhoQGFh4S2SJ13B398fW7ZsQXx8PAoKCvDqq6+iurr6ga8tlUoxf/58hISE4J///KdxjT0RtVqNL7/8Eo888ggOHTpk6eXck9zcXOzatQsymQxTpkzpcCCIa0dUq9XGh5GpK4OICFqtFpcvX4ZWq8XYsWONwmddoVca58yZM+Ho6IicnBzI5XKTBDO4Otn3338fUVFRSE1NxauvvoqkpKQHfgBIpVIsXrwYDMNg/fr1qK+v77EG2tPhJFC//fZbNDY24sUXX8TAgQMf6Bpcqxin5GgO45TL5UhPT4erqytiYmJM0u3S64xTIBBg8ODBRiXAiooKk0VFbWxuzHtctWoVoqKikJGRgQ0bNiAzM/MWrdn7wefzMWvWLAQHByM5ORlHjx416rv2NHp6QIjT+zl58iSCg4ONsYEHgeuxBG6kvEz9XlmWxcWLF1FcXIzw8PAutYndTK8zTk61Yfjw4VAqldi3b59JRr9x2NvbIzo6Gt988w1kMhlSU1OxePFiXL16tcMPAU5f9fnnnwcA/O1vf8O1a9d6nPfkBMr8/f175JmTy8O++eabYBgGzz33XJfOjDdrVZkSvV6Pffv2QaFQIC4u7oGGYd2LXmecwI2o6LBhw2Bvb4/du3dDoVCYNOHPVZF88sknSEhIQGlpKV5//XWcPHnygba4o0aNwiuvvILq6mp8/vnnKC8v71H5RG6y9aFDhzBhwgRLL+c2ioqK8MUXX6C+vh5PPvlkh1UfuxOGYVBVVYXs7GyIxWKMHj3aZFPneqVx2traGutiy8vLcfXqVZOWy3Fi0cOGDcOaNWswaNAg5OXlYePGjcjJyenwFtfFxQVPPPEEhg0bhoyMDGzfvr1Lw1RNDcuyqKysxMWLF9Hc3Gzp5RgxGAxQKpXYs2cPzp07h+joaCxatKjDQaDfw/2+XVxcuqS2eCe0Wi2ysrLQ1NQELy8vDB061GTR4F5pnDweDwMGDEB4eDiICOfPn++0msG9EIlEGDVqFLZv346goCBkZWVh6dKlHa7+sbW1ha+vL1atWgWBQICdO3ciOTnZOEfE0mi1Wuzbtw/PPPMMzp49a+nlAPhP5DMjIwM//vgjeDwePvroIwQHB3dqO8pFa+vr66FQKODt7W3SVjGFQoHU1FTodDoMHz4cnp6eJrt+rzROG5sbcz4jIiLg4OCA1NRUlJaWmuVefD4fUVFR+Pjjj5GQkIDCwkK89957yMjI6JD35PP5GD16NF588UXodDq8++67SElJ6fGlfZZCp9Ph3LlzWLVqFbRaLZ5//nnExcV1qapHr9ejubnZOBDJlMZZX1+P48ePQyAQYOzYsSa7LtBLjRO44T1HjRoFmUxmFHXW6/UmLzbnRK5HjhyJ9957DxEREcjMzMTmzZtRUVFxyzDXu/28UCjEzJkz8fTTTxsDHOnp6Rbv++Rmo3DzPCwJN9T23LlzWL9+PcrLyzF9+nQ8/vjjRknVzsDVD7e2tsLZ2blD+ssdRaPRICcnB8XFxYiNjcWAAQNMcl2OXmucwI3xeStWrIBcLkdSUpJxlJw5cHR0xNChQ7Fjxw5ERkbi3LlzWLNmDaqqqjrkBf38/LBixQpMmTIFhYWFWLduHUpLSy3qQW1tbREVFYUnnngC/fr1s9g6uD7I3Nxc/OlPf0JmZiYSExPx4osvdnmGC5dGaW5uNs4KNdWam5ubsXfvXvB4PMyaNeuW6XGmukmvhWEYqq6upuHDh1NMTAxlZ2eTRqMx2/1YliWdTkdZWVk0Z84ccnNzoz/+8Y9UUlLSoZ/X6XRUUlJC8+bNIzc3N5o1axZdvXqVDAaD2dZ8LwwGA6nVaqqrqyOVSmWRNRARaTQaOnHiBEVHR5NYLKbZs2dTcXGxSf6WWq2W0tPTKSwsjCZOnEhNTU0mWPGN392OHTsoJCSERo4cSVeuXCG9Xm+Sa3P0as9pZ2cHsViMxx9/HAqFAt9++61xurI54HKs4eHhWLNmDQIDA7F//37s3r0bLS0t9/WC9vb2CAoKwsaNG5GQkIDTp0/j9ddfR25urlm25PdDr9fj5MmTWL9+PS5fvtyt9wZubGW1Wi1SU1Px5z//GdeuXcOwYcOwdu1a9OvX744j+R4UnU6HPXv2QK1WIywszCTnTS6a/K9//QsGgwGPPfZYl1UP7ohJTd0C6HQ6SklJoTFjxpBMJqP8/HyTP8HuhEqlorNnz1JsbCwNGDCAtm7dSq2trR3ygizL0qVLl2jixInk5uZGjz32GOXl5ZFarSaWZc2+do729nZav349OTo60vfff99t9yW64XlUKhWlpqbS2LFjSSgU0pgxYyg5Odmk97h+/TqFh4dTaGgoff/99ybZIajVajp37hxFRERQXFwc5eXlkVarNcGKb6VXe07ghvccMmQIEhISoNVqce7cufsGaUyBQCBATEwM3njjDTg5OWHTpk04fvx4h1I6NjY2GDx4MLZu3YpJkybh7NmzWLZsGS5evPjQRHE1Gg2SkpLw3HPPITc3FzNnzsQ333yDuLg4k92DGzDV1NSE4OBgxMfHmyTwpVAocPz4cSgUCkyZMqXLciR3o9cbp42NDYRCIaZOnQqxWIyDBw92izwlj8eDg4MDpkyZgoULF4JhGHz++edIT083zky5F/b29ggODsaHH36IGTNmoKCgAK+88gr27NmD1tbWbjFSW1tbuLq6on///nBxcTH7/YAbBlNVVYWdO3di3bp1aGhowGOPPYZ33nkHwcHBJtnKcsjlcqSkpIBhGISHh0Mmk3V562kwGNDU1IT9+/fDz88PCxcuNItYGADYfvDBBx+Y/KoWwMHBAUqlEgcOHIBMJkNsbKzZC7q5aWyBgYHQaDT45ZdfUFxcjJiYGEgkkg59ENzd3REREYGWlhZkZGTg/PnzxuIFR0dHs073trGxgUQiQWRkJGJiYiAWi81yH+A/nSHXrl3D1q1bsX37dmi1WjzxxBN47bXXMGjQIJNW7rAsi/z8fHzzzTdoa2vDypUrER4e3uXfpVqtxv79+7Fjxw689NJLGDNmjMnnrRgx+UbZQjAMQ6WlpRQVFUVjx46l8vJyYhimW+6t0+mosrKSli5dSlKplMaNG0dlZWUdjsIyDEONjY30v//7vxQdHU1ubm40Y8YMOnXqFOn1erOdQw0GA2k0GmpqaiK1Wm2WexDdOGNrNBo6cOAAjRo1isRiMSUkJNC+ffuoubmZdDqdye+nUqlo/fr1JBaLadasWVRaWmqSa2dmZlJ8fDxFRUVRenq6WeMbfcZz8ng82NnZobGxERcuXIBcLseIESNMmnS+G7a2tnB0dET//v2Rm5uLrKwsCIVCDBw4sEOaqlyhgr+/PyIiIlBXV2dUUtBoNPD09IRIJDK5QrlWq8V3332Ht956CzKZDKGhoSa9PhFBqVSiuLgYW7duxWeffQa5XI7x48fjgw8+QFxcHJydnU3+vhiGQXZ2NjZt2gQA+PjjjxESEtKlKiODwQCVSoXPP/8cly9fxsKFCzF58mTzdvOYzewtgFarpXPnztGoUaMoKCiIUlJSzBJFuxfHjh2jwYMH06BBg2jv3r2k1WofyPPpdDq6fv06ffjhhxQZGUkuLi60bNkyOnbsGDU0NJBKpTLZ09oc0VqWZUmv15NKpaKamhratWsXzZ8/n3x9fSkuLo42bdpEDQ0NZsvtGgwGamxspMWLF1NgYCC9+OKLJsltKpVKOnXqFA0ZMoTi4+OppKTE5B7/9/Qp42RZlrRaLa1bt46kUim99dZbVFNT061rUCgUtGvXLvL09KQxY8ZQSUnJA22vWZYlg8FACoWCLl++TCtWrCA/Pz/y9fWlxMREOnLkCMnlcpN8uM1hnHq9nlpaWujgwYM0evRo8vLyon79+tGGDRuoqKiIFAqFWYsuVCoVHT16lIKCgmjkyJGUkZHR5Qc0y7JUXV1Nc+fOpX79+tF3331n1uMGR5/Z1gI3AhzcLM/k5GTk5eUhLCwM/fr167Zuf1tbW3h4eKCyshI5OTmoqalBQkICHBwcOnR/rhmYz+fD1dUVw4cPx5AhQ6BUKnHlyhWcOHECKSkpaGxshF6vB5/PB5/P71QTMRGhrq4OBoMBEydO7FQJH91UHpeTk4NDhw5h8+bN+Omnn6DT6RAfH4+33noLs2bNglQqNYsSAYder0d+fj42b96MsrIyLFmyBDNnzuxyNFWpVOLYsWPYsmULZsyYgWXLlpm0FPCumNX0LURTUxNt27aNPDw86LHHHqPi4uJuCw4R3ShHS05OpqFDh1JgYCAdOXKElEpll65ZWlpKX331Fc2YMYO8vb3JxcWFEhMT6b/+679o586dlJeXRw0NDaRQKEin05HBYLjvk91gMFBLSwsVFRWRXC6/7xo4r84wDCkUCmpsbKT8/HzatWsX/fGPf6Tx48eTVColDw8PmjlzJn333XdUWVnZpffdUfR6PZWXl9OyZcvI2dmZ5s2bR/n5+V2+LsuylJ6eTomJieTv709Hjx7tts9SnzROg8FA1dXV9Ic//IF8fHzoxRdfJIVC0W3VNyzLEsMwtHXrVnJ3d6cFCxZ0OVrIRVYVCgXt3buXYmJiSCKRkEgkIqFQSB4eHjRv3jzas2cP1dbWklqtvu/2kWEYKikpoRMnTlBVVdV916DX60mtVlNjYyPt37+fnnrqKXJzcyORSEQikYjc3NwoLi6Odu3aRUqlkrRabbfUDbMsS3K5nJYtW0YSiYRiY2MpNze3y0bERZlffvll8vLyoqeffpqqq6tNtOr7Y/oBhT0AHo8HiUSClStXoqqqCidOnMCZM2cwZswYk+m73AuuFWvmzJm4dOkSDhw4gDNnzsDX17fTWyyudU0gEGDixImIiopCcXExsrKycOXKFeTm5uL8+fPIyMiAh4cHBgwYgEGDBiEgIACenp7w9PSEl5cXXFxcjNFRbq7L9u3bsX79esyaNctYPKHX69He3o66ujrU19ejrq4OVVVVuHr1Kq5du4b6+noYDAYEBAQgIiIC4eHhiI6ORmhoqFlHHvweIkJ9fT2+/fZb/PLLL/Dz88Pbb79tHNvRFRQKBY4dO4ZTp07B29sbL730kllzwb/HhsiCDYVmhH5rQ/riiy/wxRdfYMyYMfjwww8RFBRklonGd0Kv1yMrKwvLly+Hq6srvvzySwwePNikqQO9Xo+mpiZkZ2fjypUryMzMRG5uLmpra8EwDJycnCCVSo3G6e7uDicnJ/D5fLAsi/Pnz+OXX37BvHnzEBMTA51OB51OB4VCgebmZqNxNjQ0QKlUgsfjwcvLCxEREYiNjcXgwYMxZMgQeHl5mWUY7b1gWRYtLS345z//ic2bN0On02Ht2rV49tlnu5xC0+l0KCwsxHPPPYfGxkasWbMGy5cv716Vwm7z0RaivLycZs+eTUKhkD755BNSKpXdWlze2tpKq1evJn9/f1qxYgW1t7eb/B5c+kKn05FWqyWVSkVJSUn0+uuvU2JiIgUGBpKXlxe5u7uTq6srOTs7k5OTEzk6OhKfzycbGxvi8/kkFApJJBKRs7Mzubq6kru7uzHampCQQK+99hr98ssvpNFoSKvVkk6n65ao5Z0wGAzU3t5O77//Pnl4eJBIJKL33nuPGhoaTHL92tpaWr58OQkEAlq9erXJrvsg9Mlt7c24u7vj1VdfRX5+Pv7nf/4Hfn5+mDNnjjHCaW6EQiGWLl2KM2fOIDU1Ffn5+YiKijLpMB0uSs3tCIgIcXFxCAsLg0ajgVqtRlNTE5qbm9Ha2gqNRgOGYcAwDFQqFRiGgUAggIODA+zt7WFvbw8HBwe4urpCIpHA3d0djo6OcHR0hFAoNGn9a2fQ6/UoLy/Hli1bsGfPHuMox6VLl3a5RphrY/vpp5+QlJSEoUOH4g9/+EO31R7fQrc/DixAS0sLbdy4kfr160fx8fGUnp7erc3FLMvS+vXrydvbm9auXUv19fUW8Ta/hwsyNTY2mrV8z1RwAamcnBx68sknSSKR0IABA+irr76impoak0RRlUolnT9/nuLi4sjX15d+/vlnamlpMcHqH5yHwji5WsulS5eSRCKhZcuWUXl5ebeu4dKlSxQREUFOTk507Ngxi6kf3IxaraYjR47QK6+8QufPn7f0cu4JF5FNTU2lxMREcnR0pLCwMDp+/LjJKnVYlqXy8nKaNGkS+fj40OrVq7s1Bfd7en3LWEfg1PrWrFmDCRMm4MiRI/jhhx/Q3NzcbeoDAQEBeP755+Hr64vdu3ejoaHB4vq1BoMBOTk5+Pnnn82mXthVuKjxkSNHsGbNGixbtgylpaWYNWsWtm7dipEjR5okEEVEKC8vx9///nekp6djwoQJWLFiRbcFD+9Enz9zctjY2KBfv35YuXIl8vPz8dNPP8Hb2xtPPvkk+Hy+SduV7oSrqysmTJiAvXv3Ij09HceOHcOCBQvM1gvYEYgIer0eCoWixzR50286s3q9Hm1tbWhoaMCuXbuwf/9+1NfXQyqV4tlnn8W0adMwaNAgk9xTr9dDqVRi79692L9/PwIDA7F8+XIEBARYdIbMQ+E5OYRCIWJjY7F8+XLI5XL87W9/Q15enknV4u+GjY0NfH19kZCQgIqKCnz//fdobGy0uDSmg4MD3NzczDbt+UGg32Qsm5ubkZubi82bN2PGjBn48MMPUVdXh8mTJ+Nf//oXVq1aZTLDBG5055w+fRrbt28HwzD485//jLi4OIvLhfbZPOfd0Ov1aGlpwaeffooff/wRYWFh+PTTTxEREWH2PwbDMKipqcFLL72EtLQ0LFy4EG+++SZ8fHzMet+7YTAYUF5ejpKSEoSFhcHX19ek16cbMY1bvm5+jWVZGAwGMAyDlpYWlJaWIikpCRkZGSgpKYFcLodIJEJ8fDxmz56N+Ph4SCQS2NnZmcyjKZVKJCcn44033oCNjQ1WrFiBpUuXwtHRsdvztr/noTNOjtLSUmzcuBG7du3C8OHD8d///d8YOHCgWZUHODIzM/Hyyy+juLgYq1evxrJlyyAWi82+tf49BoMBarUajY2NkEgkD5wuYFnW+KXT6aDVaqHVaqHT6cAwDLRaLdrb26FUKqFQKG7RFTYYDKivr8f169dRUVGBxsZGtLW1obm5GXq9Hp6enhg/fjymTp2K0NBQeHp6mmxAEPCfLX1GRgY++OADZGdn47nnnsPKlSvh4+PT7X+Luy3yoaWgoICmTZtGYrGY5syZQ5WVld0taY6IAAAUzElEQVQSnWMYhg4dOkQymYxCQ0Np27ZtpFQquz2Cq1QqacuWLRQWFkZ79+697/ffXPjOpWAKCwvpwoULtGfPHnr//fdp7ty5NGzYMPL39yeBQEC2trZkZ2d3y5e9vT3x+Xzi8/nk5OREPj4+FBoaSrGxsfTUU0/Rjh07zN5aptPpqKKighYsWEAuLi60aNEiKioqMtv9OsNDExC6E4GBgfjkk0+wdu1apKam4s0338SGDRsgk8nM+uS0tbXFqFGjsH79enz00Uf4/PPP0dLSgqVLl0IqlXbbU5tlWcjlclRUVECpVN7z+xiGQVtbGy5fvowLFy4gPz8ftbW1kMvlaG9vN45htLGxgaurK0JDQzFq1CiIxWKIRCJjySC3KxEIBJBIJJBKpXBycoJIJIJIJIJEIoGTkxMcHR3N9nvQ6XQoLS3F22+/jQsXLmDChAn44IMP4OfnZ5b7dZaH2jgFAgHCw8PxySef4LXXXsPhw4chFArx7rvvwt/f3yyDVoEbgRhnZ2fMnTsXDMNg8+bN+Otf/4ry8nK8/PLL6NevH/h8freE8e802Zp+C8zodDo0Nzejvr4ep0+fxq+//orS0lLI5XIYDAbY29tDKBRCKpUiMTERkZGRCAsLg0QigYODwy0VR7a2trfcx9bWFnZ2dt1WqcW9L4ZhUFhYiA0bNuDMmTMYOnQo1q5da5JCeZNjYc/dI2BZllJSUigmJoa8vb3p5ZdfppqaGrPLUBDd2Fru3r2bIiMjycnJicaNG0fHjh2j5uZmYhjGrJVEKpWKvvvuO5owYQIdPXrUWKOrUCgoPz+f9uzZQwsXLiQfHx/i8/kkkUgoJiaG5s+fTx988AHt3buXCgsLzToCw1RwKhmFhYX05JNPkrOzM02YMIHOnTtn6aXdlYc2IPR71Go1Ll26hDfeeAOlpaUYNmwYNm3ahODgYLNGcVmWhVqtRlFREf7+97/jyJEj4PP5mDx5MpYvX47IyEjY29ubZYvHsiza2trQ1NQEd3d32NnZ4cqVK/jHP/6BtLQ01NXVgWEYSKVSTJo0CRMmTED//v3h7u4OgUAAPp8Pe3t7k0ZPzYVWq0V+fj7eeOMNXLlyBSNHjsSf/vQnBAcHmzTQZEqsxvkb9FtoPzMzE+vWrUNaWhoSEhKwbt06REVFmc1AbqasrAwHDhzATz/9hNbWVkilUmMKwcfHB1KpFAKBwGTbXa1Wi4qKChQWFsLGxgbJyck4cOAAWlpaYG9vj8DAQDz66KN49NFHIZPJIBaLLV70/qBwhey5ubnYtGkTzp49i1GjRuGdd94x/l17LBb12z0QlmUpIyODpk6dSmKxmCZPnmwslO+OaCq39XrnnXcoKiqKRCIR9e/fn55++mnatWsXFRQUUFtbG6lUKtJqtcQwDBkMhnvKkrAsa4y0cq1lKpWKSktLadWqVcTn80ksFpOTkxOFhobSkiVL6Mcff6S2trYeUQPcWbh5LMnJyTRr1ixycXGhOXPm0MWLFy29tA5h9Zx3QKvVora2Fhs2bMDBgwfh5uaGTz/9FGPHjjW7kgL9Foxpb29HZWUlkpKS8O2336KiogJ2dnaQSCQIDg5GbGws4uLiEB4eDrFYDD6fDzs7O9jZ2d3i4bk8pMFggF6vh0ajQVFREfbt24fTp0+jqKgITU1NiIiIwDPPPIOJEycaI6jmjJiaGyJCa2srjh49ik8++QSNjY2YNGkS3nnnHfj7+5tPpd2EWI3zHhQWFmLLli3YtWsX/P39sXLlSkybNg0SiaRbyt24fsuSkhKcOHECZ8+eRXl5Odra2sCyrLHHMjAwEEFBQZDJZPD19TVKhLAsC5VKhfb2djQ2NqKqqgoVFRUoLS1FS0sL+Hw+iAgtLS3YsGEDFi5cCDc3tx5/frwX9FtxQXV1NQ4dOoRt27ZBpVJh2rRpWLlyJYKDg3tEqWJHsBrnfSgvL8c333yDH3/8Efb29pg/fz6WLFmCgICAblGT5yAiaDQapKamIicnBwUFBaisrERlZSVqamqgVqthMBju2OnCpUt4PB6cnJzg7++PAQMG4JFHHoGjoyMKCgqwYMECk074sgREBK1Wi/Lycnz99dfYt28fHBwc8MILL2DevHkmL080N1bjvA8Mw0CpVOLUqVP47LPPkJ+fj7i4OLz99tuIj4/vlnI/DvpNF4lTMeD0fjQaDcrKylBcXIyysjKjZ7Wzs4Orqyvc3d3h7e2N/v37w8PDAw4ODkblAyKCSqWCs7Nzt4lymQP6LYeZm5uLt99+G5mZmQgJCcH777+P4cOHw8nJqeflMe+D1Tg7ABFBLpfj0qVL2LJlCzIzM+Hl5YWXXnoJ48aNg4eHh0W3SpzH4L5YljVW63DJfk565OaHiVarxdmzZ3Hy5EnMmTMHjzzyiMXeQ1fQarVoamrCr7/+ii+//BIVFRUYPnw4Xn/9dURFRfXes3N3Rp96OwzDUFVVFa1Zs4YCAwPJx8eH3n33Xbp69apJZ5h0F5acbG0KDAYDKZVKys/Pp7fffpuCgoLIx8eHVq5cSUVFRb3u7/F7euHjxHLY2trCy8sL69atw8aNG2FnZ4cvv/wSTz31FP79739DqVRaXN3gYYHrhPn3v/+NJ554Al999RWEQiH+8pe/YNOmTQgMDOyd3vImetcm3MJw20QnJydMmzYNMpkM33//PS5cuIA333wTU6ZMMeq/coNvezI8Hg9isRihoaGWUZfrBPTbEN6ioiL8/PPP2L9/P/R6PebMmYMlS5YgIiKi17yX+2E9c3YBlmVRXV2N48eP4+uvv0ZRUREiIyOxaNEiTJ8+HRKJBAKBoMc+wRmGQWlpKXJzcxEbG9upQUbdBecpFQoFUlJS8I9//AOnT59GQEAAXnjhBcycOdMiwtbmxGqcXYRL7jc3N2P9+vU4ePAgFAoFEhMTsXbtWkRERPTYgASXB21tbYWbm1u3jKroLGq1GmVlZdi8eTMOHz4MlmUxdOhQbNiwAYMGDer0pLWejNU4TYRer0dtbS1Onz6NAwcOIDs7Gw4ODpgyZQpmzpyJiIgIODs79ygj5Wal7Ny5E6+99homTZpk6SXdAvfwKCoqwuHDh3HgwAE0NDQgLCwMEyZMwPTp0yGTyXps4XpX6Tt7AAtjZ2cHf39/zJ07F8OHD8ehQ4fwww8/YMeOHcjIyMCMGTMwe/ZsSKVSY6+mpZ/yer0e169fR1JSEhYuXGjRtXDQ73pJf/nlF+zevRsFBQUQCARYsmQJZs+ejQEDBvRZozRiuUBx34QrMNdqtVRZWUkbNmygsLAw43i8Q4cOmUydvKv0xFSKVqulqqoqOn78OE2ZMoXEYjEFBQXRG2+8QUVFRaTRaCw2n6W7sW5rzYhWq4VCoUBeXh6OHj2KM2fOQKlUon///oiOjsaoUaOM0cXuLAXk0Gg0OHjwIPbu3YsXXngBiYmJ3Xp/Dq1Wa5RAOXfuHDIyMlBcXAxnZ2eMGDECU6dORXR0NFxdXXtFwbqpsBpnN9HQ0ICcnBzs2bMHR44cAcuy8PHxweDBg/HYY49h6NChcHFxMUp7dMe212AwoLW1FbW1tfD19YWbm5tZ7wfcKhrNPbwuXbqE/fv3IzMzE/X19eDxeJg0aRLmzp2LiIgIi0mHWhqrcXYT3IeSiFBcXIwffvgBhw8fRllZGbRaLYKDg7Fo0SKMHz8egYGBcHd3N3tJoMFgQE1NDa5fv46QkBB4enqa9X7cPVtbW1FRUYG0tDR8++23yMnJgY2NDfz9/TF16lQsXboUgwYNuk136GHDapwWQKPRQKFQoKysDBcvXkRSUhJSUlJARHBxcUFAQAAGDx6MRx55BCNGjDCO4DO1sapUKmzbtg1fffUVNm3ahNmzZ5v0+gCM+rVtbW3IyspCWloa8vLyUFpaiqamJjAMgyFDhmDixIkYMWIEQkND4ezs/FBtX++GNVprAThlOg8PD4SHh2Py5Mm4cOECjh07hrS0NGRlZSE7OxuHDx+Gj48PRo4cifHjxyM0NNTYTcI1V988l/NBYVkWSqUSFRUVUCgUXXpPXEM3p+Cu1Wqh0WhQX1+PX3/9FadPn0Z5eTmam5thMBggEokQGxuLyZMnIzExEf7+/hCJRA+tl7wTVuO0MI6OjujXrx8CAwMxf/58NDY24uzZszh27BiysrJw9epVnDt3Dp999hmkUilGjhyJESNGICYmBt7e3sZR8pb+UGs0GjQ0NKC2thbFxcVIT09HSkoK8vLyoNFo4OrqCplMhtGjR2PixIkYP378LRVJll5/T8S6re1hcFIiSqUSDQ0NqK6uRn5+PrKyspCTk2McW8jn8yEWi+Hu7g4fHx8EBwcjMDAQAQEBkMlkcHZ2NmrGcl729zAMg8zMTKSlpWHixIkYPHjwbd/DeUO9Xg+9Xm/0jAqFAnV1dSgrK0NOTg6Ki4tRV1eH5uZmtLe3w8bGBgKBAAMHDkRcXBwiIiIgk8ng5eVl3Lb2FkUCS2E1zl6AUqlEW1ubcdhPWloa0tPTUVxcbBwbz+fzjdtloVAILy8vBAUFoX///pgxYwZ8fHxuE3BmWRYajQZyuRwuLi63lO9xEdXCwkIUFBSguroaVVVVqKmpQU1NDVpaWqDVaqFWq6FSqQAA9vb2kEqliI6OxvDhwxEVFQVPT09jaWBPbwToaViNs5fCsizq6uqQnZ2NzMxMlJaWor6+Hs3NzWhpaUFLSwtaW1uh0WiwevVqLF68GIMGDbrFg+p0OqSkpCApKQmPP/44oqOjb3mtrKwMTz75JC5evGiUOhEKhXB2doaLiwucnZ3h5uaGkJAQxMbGYujQoRgwYIA1mGMirGfOXgqPxzOOQRgxYgQYhoFGo4FKpTJ+1dXVYcOGDdi5cycCAwMREhJyi3EyDIP09HRs27YNgwcPvsU4lUoldu3ahYqKCkyZMgWzZ8+Gp6cnnJycjB7awcEBjo6OcHZ2hkAggEAg6Nk6sL0Mq3H2YjgpzLtp/8jlchw8eBBHjhzBtWvXbpteTb9pEsnlcuh0ulteU6lUOHjwIPh8PhYsWID58+cbiyOsdA89p0XCismxtbVFcHAwAKC6uvo2lQZusjWne3szbW1tyM7Ohre3N2QymVF/yEr3YfWcfRgejwcvLy/Y29sbpTNvxsHBAYsWLUJiYuItaQ0iQlNTE/R6PXx9fbulcsjK7Vg9Zx+GO5fy+XxotdrbtrUAwOfzIRQKb/OKLS0tICJ4e3vD3d29u5Zs5SasxtmH4fF48PDwgL29PRiGuc1z6nQ6HD58GK+++irS0tKM/0+/6fQAgJubG1xdXbt13VZuYDXOPgxnnHw+/47GybIsqqqqkJGRgaamplteU6vVxiG/vW2yWF/Bapx9GB6PB3d3d9jb20On091xWwvc8JQ3p7uJCEqlEjY2NhAKhT1KWuVhwvpb78PY2NhALBYbjfP3npPH48Hf3x/Dhg2Dh4fHLa9xxtnnpUB6MNZobR/GxsYGfD4fIpEICoXiNs8pEAgwZ84cTJw48bZzJfe9fUlqsrdh9ZwPAXfr+NDr9bhy5Qr27t2L8vLyW17jChs0Go3Z12flzliNsw/DVQAplUoIBILbvKBOp8OxY8ewevVqZGRkGP/fxsYGIpHIKE1pLb+2DFbj7MPQb4NxdTrdXdvG7oajo6MxMPT7s6qV7sFqnH0YlmVRX19vNM7fFxrweDwIBAK4u7vf1knCBYLkcnmXVRKsdA7rab8PYzAYUFdXB61We0fPaWdnh8mTJxt7MDm4/CZwQzWwpaUFYrG4W9duxWqcfRqWZVFbW3tX47S3t0dYWBhCQkJua/XipE9qamrQ0NCAoKCg7ly6FViNs09jMBhQWVkJhmHuOHadG2n4+1ymjY0NJBIJfHx8jMoHVrof65mzD0NEqKiogK2tLby9vR+o5cvBwQGjRo1CW1sb6urqzLhKK3fD6jn7MCzLgmEYyGQyDBky5IGitSKRCI8//rhJZDOtdA6rhlAfRqfToaCgAM3NzQgMDIRMJuuw92QYBk1NTSgsLISfn5+xadtK92E1zj7MzXNJ7lb0zg2c5fF4sLW1tZbr9SCsf4k+DDeXpLCwEM3NzXf8Hh6PBycnJzg5OcHLyws+Pj5WgecegtU4+zg8Hg8NDQ3461//irKyMnh4eCA+Ph5DhgyBk5MTWltbUVVVhdzcXNjY2CAgIAAzZ85EVFSUtcnawliNsw9jZ2cHiUSCyMhIyGQynD17Fp6ennj11Vfh4eEBHo8HhmHQ1taGzMxMbN682TjXZOXKlZgzZw4cHR2tcpcWwmqcDwEikQgeHh6wtbWFm5sbfH19YWdnZ1Tfc3Z2No50WLduHU6dOoV3330Xer0ec+fO7Za5nVZux5rnfMjggj/cuZILCNna2iIkJAQff/wxRo8ejfb2dnz00Uc4ffr0bZq2VroHq3FaMeLg4IDQ0FAsXboUXl5eKCsrM6q+W+l+rMZp5RZsbGwQGRmJqKgoAEBycjIuXrxo4VU9nFiN08pt+Pr6IjAwEADQ1NSE2tpaC6/o4cRqnFZuQygUon///gBuVBlZjdMyWI3Tyh25uVPlbgUMVsyL1Tit3BGGYYz/turWWgbrb93KbajVahQXFwO4MUvl5iFHVroPq3FauY2qqiqjcXp6ehrPn1a6F6txWrmNvLw85ObmAgDGjRuHuLg4C6/o4cRavmfFiE6nQ2NjIw4cOICamhpIpVJMmzYNPj4+ll7aQ4nVOB8Cbh5UxPV43hzkYVkWBoMB9fX12LJlC06cOAEnJyc888wziI+Ptxa+WwircT4EaDQaNDc3g2VZqNVqtLa2QiQSgcfjQa/Xo729HdeuXcPXX3+N5ORk+Pv7Y9WqVZg+fTpEIpGll//QYlVC6MNoNBpUVlYiKysL27ZtQ1FREfz8/PDoo4/Cy8sLzs7OaG1tRXV1Na5fvw47OzuEhoZi/PjxGDBggLUbxcJYjbMPo9FoUF5ejoqKCrS2tt7xe3g8HhwdHeHu7g5fX1/4+flZlRB6CFbj7MMQEfR6PQwGw13nnVg1hHouVuO0YqWHYs1zWrHSQ7EapxUrPRSrcVqx0kOxGqcVKz0Uq3FasdJDsRqnFSs9FKtxWrHSQ/l/DJ99mIHNY7oAAAAASUVORK5CYII=)
The maximum value of l to produce a minima at D is given by
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed
![](data:image/png;base64,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)
The maximum value of l to produce a minima at D is given by
physics-General
physics-
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed
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)
The maximum value of
to produce a maxima at D is given by
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPkAAAEECAYAAADqNJLjAAAgAElEQVR4nOy9d1hU1/b//55eGGboQxOpIhZEFEHFghpjLDGWGL0m6jUaNTFFb2yxRhM18WPaVaOxxCR+1XhN1GDHigXBgigogtL7DExhetu/P5Jzfhg1ERmKZF7PM48+h5l91ilr77XXXmttBiGEwIEDB60WZnML4MCBg8bFoeQOHLRyHEruwEErx6HkDhy0chxK7sBBK8eh5A4ctHIcSu7AQSvHoeQOHLRyHEruwEErx6HkDhy0chxK7sBBK8eh5A4ctHIcSu7AQSvHoeQOHLRyHEruwEErx6HkDhy0chxK7sBBK8eh5A4ctHIcSu7AQSvHoeQOHLRyHEruwEErx6HkDhy0chxK7sBBK8eh5A4ctHIcSu7gIWw2G0wmE6xWa3OL4sBOOJTcAY3NZkNNTQ3u3bsHhULR3OI4sBMOJXdAYzabkZSUhHfeeQfnzp1rbnEc2AmHkjugIYTAarXCaDQ6zPVWBMOx4aEDCkIItFotVCoVJBIJRCJRc4vkwA44RnIHNFarFXK5HOnp6aisrGxucRzYCYeSO6CxWCw4efIk3n//fVy4cKG5xXFgJxxK7oDGZrPBaDRCLpdDp9M1tzgO7AS7uQVw0HTYbDYYDAaYzWZYLBbYbDZYrVZYrVbYbDbodDpUVlbCYrGguroa+fn5YLFYYDKZD/1Lffh8PjgcDhgMRnNfmoO/wOF4ayUQQmAymR766PX6hz4qlQolJSWorKyEVquFXq+HTqeDXq+HwWCARqNBRUUFqqur4erqCj8/P/D5fPojEAggEAggFAohFosREBAAqVQKoVAIoVBI/43P54PNZoPD4YDL5YLNdowlzYlDyVsJRqMRd+/eRUZGBrKzs1FRUQG5XE5/qquroVarQQhB3UfOYDDA5XLB5/MhFAohEokQHh6OgoICKBQKGAwG6PX6xy6rMRgM8Pl8uLu7w9PTEx4eHvD09ISPjw8CAgIQEhKCrl27wtvb2zHaNyMOJX/OsNlsUKvVUKvVtCc8LS0NGRkZqKmpgclkgs1mo0dRLpcLsVgMf39/BAQEIDAwEN7e3nBycqJHYDabDSaTCYvFgps3byI5ORkJCQno1q0bbDYb/TEajdDpdNDpdFCr1cjPz0d+fj4KCwtRVVVFWxBmsxmEELBYLIjFYkRERKB3797o0aMHfH194eLiAoFA4BjhmwjHXW7hmM1mGI1G1NbWorKyEiUlJbh69Spu3ryJnJwcGI1G2Gw2CAQCeHh4wMvLC2FhYWjbti0CAgLQpk0beHh4gM/ng8vlgsPh0ErNZDLBYDDoUVav1yMlJQXHjh1Dz5490aFDh4dkIYQ8pPR1pwYKhQJFRUUoKChAYWEhCgsLUV5ejurqaly5cgVXrlyBUChEeHg4evTogY4dO8LX1xdSqRQSiYSWz4H9cSh5C0cmk+H8+fM4e/Ysrl+/juzsbOj1egiFQrRr1w59+/ZF165dERYWhsDAQPj6+kIgEDzTuQghsFgs0Gq1MJvNj/ydwWDQTjcA4PF49N98fHwe6hSsViuqq6uRm5uLrKwsXLlyBZcuXcLhw4dx8OBBODs7o23btujUqRNeeOEFDBw4EG3btn0muR38NQ4lb0FQEWc1NTXIzMzEoUOHcPnyZTpZRCgUol+/fhg+fDh69uwJV1dXCAQCehRks9m0Aj4L1PzcxcXlIQV+FphMJtzd3SEWi9GpUye8/PLL0Ol0ePDgAc6fP49Lly6hpKQEp0+fRnJyMj777DP07t0bI0eORGRkJDw9PWkHnoOG4ZiTtwAMBgO0Wi3y8/ORlpaGY8eO4ebNmwAAkUgEPz8/dOnSBQkJCejevTucnZ3B4/HsrgBmsxlZWVm4cOEC4uPj0bVrV7u2T1kKer0eCoUC6enpOH36NO7cuYOSkhJoNBpwOBy0b98eAwYMQFRUFNq3bw93d3fw+fwGdWD/ZBxK3oxQnu47d+7g559/xpEjR5CTkwOLxYLQ0FC88sor6NOnDzp27Ahvb+8mGdX+7HlvbGw2G4qLi3Hnzh0kJyfj8OHDyMnJgdVqha+vL+Li4vDGG2+gX79+cHZ2dnjpnwGHkjcT1dXVKCgowP/7f/8Pv/32G4xGI/h8Pjp27IjXX38dsbGxcHJyok1xFovV6C+40WjEb7/9hu3bt2PmzJl45ZVXGvV8FGazGSaTibZoMjIycOjQIaSkpEClUoEQgri4OMyePRsdOnSAq6urw0lXDxwTnibEYDBArVbjzp07OH36NE6fPo2qqipIpVJERkZi0KBBiI2NhZubG4RCYZPLZ7VaUVlZibS0NIwcObLJzsvhcMDhcODk5AQ3NzdIpVL07NkTGRkZOH78OFJTU5GRkYG3334bCQkJePHFF9GtWze4uro6zPinwKHkTQC19JSXl4edO3fi4MGDqKysRGRkJObNm4eePXsiJCQETk5OzS0qgN9N6OYy8BgMBng8Hng8HgYOHIj4+HgUFhbi7Nmz2LNnD7Zv344jR44gLi4OU6dORe/evSEUCsFkOtIwnoRDyRsZrVaL0tJS7N+/Hz/99BNMJhP8/f2xdOlSJCQkQCwWg8fjgcPhNLeoYLFYcHZ2RnBwMFxdXZtbHAC/j/KBgYEYP348hg8fjtTUVOzZswdZWVmYOXMmRowYgbfeegshISHg8XgOZX8Mjjl5I0AIgU6nQ2FhIS5evIijR48iIyMDPj4+GDRoEMaPH4+2bdtCKBS2KEeS1WpFeXk5cnNzERISgoCAgOYW6SFsNhvMZjOqqqpw/vx5/PLLL7h79y78/PwwevRo9O/fHwEBAXB2dm5uUVsUDiW3I5S33Gg04syZM1i/fj1u374NLpeLV199FZMmTUL79u2bZb79NFCdk0qlglgsbtGVYSwWC6qqqrBv3z5s2rQJMpkM3bt3p0d3KmuuJXWizYVDye2ITqdDSUkJfvrpJ+zevRsGgwGxsbF4++230bVrVzg5OYHL5bZYk9JgMGDXrl1Yt24dFi9ejEmTJjW3SE+Eqken0WhQXFyMDRs24PTp0zCbzRg4cCDeeusttG/fHi4uLs0tarPjmJPbAUIIZDIZkpOTsWvXLty6dQve3t54+eWXMW7cOPj4+DxzqGlTYrPZoNfrUV5eDo1G09zi/CUMBgNsNptOdlm6dCmioqKQmJiIs2fP4v79+xg/fjyGDh0KX1/ff/SSm0PJG0Dd0eSrr77Cvn37UFpaiuHDh2POnDno0aNHk6xv2xMmk0knsDwv8Hg8+Pv746233kJCQgJ2796NrVu3YvXq1cjIyMCSJUvg4+Pz3D0Le8FasWLFiuYW4nlFrVbj8uXLeO+995CUlARXV1fMnz8f8+bNQ2BgILhc7nP1UhFCUF5eDrVajYSEBISFhTW3SPWCwWBALBajW7duaNeuHbKzs3Hx4kVcvnwZbdu2hZeXF9hs9nP1TOyBY07+DJjNZqjVaiQmJuL7779Hfn4+evfujQkTJqBfv35wcnJqEYkV1Hr30zqgrFYrdDod5HI5XFxcWswyWn2hph3Xrl3D1q1bcfHiRXh7e2PixIkYOXIkPD09n4vpk71wKHk9sVqtqKmpwc6dO7F582YYjUbMnj0b//rXv+Dv79+kZu6f87upY9Qj1Wq10Ol0cHZ2Bp/PB/BwPDqVS85gMMBkMmGz2ZCfn49bt26hS5cuz91I/mcsFgvkcjm2bNmC7777DhaLBcOGDcPChQsRHBz8jzHfHUpeT6iota1bt8Lb2xtvvvkmJkyYAGdn5yZ17lCVWoqLi1FSUkLnbRcWFqKkpISuEkMIAYPBgEAggFgshlgshouLC7y9veHv709XivH29oarqysSExOxZs0aLF++HFOnTm2y62kMKJ9JbW0tzp8/jw0bNiAzMxORkZFYuHAhevbs+Y8Y0ZvfpnxOMBgMyM3NxaZNm3Dy5EkEBgbi3XffxYsvvgg3N7cmy9gymUwoKSlBSkoKMjMzkZubi8LCQlRXV4PNZoPNZkMsFtNhslwuF0ajkS7mSFWYuXPnDqxWKwghkEgk8PHxgb+/PyorK1FVVYWysjLIZDI4OzuDw+E8l/HhdT3wAwYMgIeHBzZu3IiUlBR88sknmD9/Pnr27AmJRNLcojYqjpH8KTCbzcjJycHChQuRkpKC4OBgfPHFF4iOjm6SwBZCCF0GKisrC2vWrMHVq1ehVCrBYDAglUoRHx+PhIQEdOrUCS4uLg9lr1ksFlgsFrr+mkajQUFBAe7du4eMjAykp6ejoqKCVnqr1Yrg4GAMHz4cI0eORKdOncDj8ejKMFRp5ucNi8WC8vJyLF++HP/73//g5+eH1atXY9iwYc+dk7Q+OJT8KUhLS8Mnn3yC5ORk9OnTBx999BGioqJoJWpMCCHQ6/U4efIk9u3bh3PnzsHFxQVBQUHo0aMHXYtNKBTS8lBzTepDzdPrfqh661SaZ1VVFW7evIm0tDTk5+fjwYMHqK6uBpPJhLe3N6Kjo9GtWzdEREQgODgYbdu2fe4UneosCwoK8PXXX+Pnn3+GVCrFnDlzMGHChBaTIGRvHEr+F+j1eqSlpWHt2rW4ffs2Bg4ciLlz5yI8PJwe2RoLSrmLioqwe/duJCYmQqlUIi4uDkOHDkV0dDTatGlDl0hqiMOPcuDp9XoolUpkZ2ejqKgIxcXFyM7ORl5eHhQKBUwmEzw9PREUFITw8HCEh4cjODgYvr6+EAqFcHJygkAgaPFr7AaDAYWFhfjqq6+QmJgIZ2dnzJo1C+PHj4enp2frG9GJg8diNBrJ9evXSa9evYi7uzsZM2YMKS4uJmazudHPbbVaiV6vJ6mpqWT48OFELBaToKAgsmHDBiKXyxtNBqPRSE6ePElmzZpFTp8+TUwmE6mpqSH3798nv/76K5kyZQoJDAwkIpGIODs7E6lUSoKDg0lsbCyZO3cuOXjwIJHL5aS2tpZotVqi0+mIXq8nRqORmM1mYrFYiNVqJTabrVHkrw9ms5lUVlaS999/n4hEIuLh4UFWrVpF1Go1sVqtzS2eXXGM5E/g3Llz+Pjjj5GRkYFRo0Zh8eLFaNOmTZMEU9TU1ODUqVNYt24dZDIZevTogVmzZiE6OhpOTk6NtvSj1+uxc+dOrFy5EitXrsS0adPorZQsFguMRiM0Gg3u3LmDGzduIDMzE6WlpSgpKYFKpaJLQ4eGhqJdu3YICgpCmzZt4OXlBQ8PD7i6utJbIjf39krkjylLcXExNm/ejK1bt0IsFuPtt9/G7NmzW2wS0bPg8K7/CZ1Oh/Pnz+Ozzz5DXl4eJk6ciPfffx8BAQGNHuBCCEF1dTUOHjyIL774AgwGA2+88QYmTpyIwMDAJpki1C3JXLcEM5fLhVAohEQigVQqRa9evVBTU4OSkhIUFxejtLQUDx48QF5eHkpLS3H27FkkJSWBw+FALBZDIpHQH6FQCB6PBxcXF3oXFoFAAJFIBFdXV7i6usLd3R1ubm4QiURwcnJ6qD68PaA8735+fpg5cyasViv27NmDLVu2wNXVFWPHjn1ug4H+jEPJ62A0GpGZmYmPPvoIpaWleOmll7Bs2TK4ubk1iYPNbDbjzJkz+Prrr1FeXo4lS5bg3//+N9zc3Br13BTUi0+NtI+DyWTSO7NQtdMB0N57nU4HmUyGjIwM3LhxA+np6cjOzkZubi59ndS5JBIJNBrNI157FosFgUCA2NhYDBkyBAkJCbQFQ53fXs+Dy+UiICAAixcvBiEE27dvx7JlyyAUCjFmzJhG71ibAoe5XofU1FQsXrwYN2/exBtvvIF58+bBy8urSSKj9Ho9cnNzMWvWLMhkMsyYMQNTpkyBRCJpshBZq9WKkpIS5OTkoF27dvXa7ID84bWvu1OqxWKh/62trUVNTQ0UCgU0Gg10Oh0dHkxtvaTRaCCXyyGTyVBWVoaysjJYLBaIRCKEhoaiU6dOiI6OxuDBg+Hj42M3Bx9luhcWFmLjxo3Yvn07QkNDsWjRIowYMaLBNeibG4eS4/cR/P79+1i6dClSUlIwcuRIOsmkKZaJCCHIzc3FnDlzcPfuXbz66qtYsGABxGJxk8bAW61WaLValJeXw93dHR4eHnZpt24HQH3qHqP+tVgsUKlUUCgUqKqqQkFBAbKzs3H37l0UFxdDp9OBzWYjLi4OI0aMQM+ePSGVSu022lIRhP/3f/+Ho0ePws/PD+vWrUNkZCTEYrEd7kQz0aRuvhaI2WwmJSUlZMaMGcTb25v07duX5ObmEpPJ1GQyqFQq8tFHHxE+n0/GjBlDsrKymuzcddHr9WTr1q0kLCyM7Ny5s1lkqIvFYiE6nY7IZDJy6dIlsmjRIhIWFkY8PDyIn58fGT16NLly5QpRqVTEaDTaxWtvMpmITCYj06ZNI+7u7iQ6OpqkpaURk8nUIlYFnoV/fKqpTCbDTz/9hO3btyMiIgKffvopOnTo0GTeX5vNhj179mD37t0ghGDVqlXo2rVrs2SxmUwmXLt2DUePHkXfvn3RvXv3JpehLtRcncfj0WWax40bh27dusFsNuPSpUvYv38/CgoKIJVK4eHh0eCCmEwmEzweD+Hh4aitrcXFixchl8sRGRkJV1fXFh8D8Dj+sUpOpVX+/PPP2LJlCzw8PLBkyRL06tWryZwttbW1SE1NxapVq6DX67F06VIMHDiw2Wqrmc1m3LhxA0lJSRg4cCBiYmKaRQ6KuhlybDYbPB4Pzs7OCAoKQnR0NIKCglBWVoYbN27g+vXrkEgk8PLyatDyF3U+Z2dnhIWF4fbt27h79y5sNht69Ojx3BXUAPDPNdd1Oh05duwYiYqKIgEBAWTbtm1EoVA02fmpYJvOnTsTLy8vsmjRImIwGJo1EEOn05Ft27aRdu3atQhz/a+w2WzEZDKR7OxsMmHCBOLh4UECAgLIpk2biEKhIBaLpcHn0Ov15Pr16yQ6Opr4+fmRY8eOkdraWjtI37T8I5XcZrOR/Px8MnjwYNK2bVuyYMECIpPJ7PJiPO3509PTyYQJE4hAICAzZswg9+/fb/Y5n9VqJWq1mhQWFhKVStWssjwNNpuNGI1GUlFRQb7++msSGhpKfHx8yPvvv09KS0sbfD+tVivR6XRk48aNJDQ0lERGRpJz587ZSfqm4x9prstkMmzatAmHDx9G3759sWDBAkil0iaZB2u1Wjx48AArV67EtWvXEBkZiaVLlyI4OLjZq8lQ2yRlZWVBKBS2+GCQunN2KsLu1q1buHr1Kj2PbsgmiVTcgFQqhVwux8WLF6HRaOj92J4Xs/0fpeTkj5roiYmJ+Pzzz+Hp6YmVK1eiU6dOTaJgOp0O2dnZmDNnDq5fv47OnTvj22+/RVBQUKOvxdYNTTUYDHRuuVqtpj8ymQw///wzlixZAolEgjZt2qC2tha1tbXQarXQ6/V0uqrFYqELUjT3y04Fz7Rr1w5dunTBpUuXcPHiRdTU1CAuLq5BO6swGAyIRCJERETg1KlTyMzMBJ/PR3R09HMzP/9HrZMbjUZcv34d8+fPR35+Pj7++GOMHTu2yWpzHzp0CN988w1SUlLw6quvYs6cOejUqVOTBNvU1NTg7t27yM/PR0lJCcrLyyGXy1FTU0Mrr9FohEwmQ0VFBaRSKaRSKTgcDrhcLvh8PlxcXODp6QmpVAo/Pz8EBgYiPDwcvr6+LSIqjPyRuXft2jXMmzcP5eXlmDJlCj744IMGRQ0SQmAwGHD16lXMmzcPlZWV+OKLLzBo0KDnYv38H6PkNpsNMpkMS5YswdmzZxEfH4+1a9fCw8OjUUdxm82Gmpoa2ouvUCgwcOBALFiwAEFBQXTtNXtB/og/VygUUKlUyMzMxLVr15Ceno6qqirU1tbCZDIBAB2eSo1ITCYTWq0WxcXF8PPzg5ubG0wmEx3BZjKZ6JJSLBYLYrEY7u7u6NixI2JiYtC5c2d4eXlBIpE0W1klStHPnDmDefPmwWQy4ZtvvkF8fHyDKsBYrVbo9Xps374dmzZtgre3NzZs2IDOnTvbUfrG4R+j5BqNBkePHsV7772H8PBwbNmyBSEhIY220SC1b1dlZSV++OEH/Pe//wWfz8e4ceOwaNEiiMViu52bqhqj1+uhVqtRWlqKo0ePIikpCWVlZSCEgMvlQiAQQCKRIDQ0FO3bt0dERATCwsLg5uYGPp8Pq9WKM2fOYP/+/Rg/fjwGDRpEj2JKpRL5+fl0BFp2djYUCgV0Oh2MRiMYDAbc3d3Rp08fDB06FO3bt4ezszOcnJzA4/GatP4dpeg7duzAJ598grCwMGzatAkdO3ZssHmdn5+PpUuX4tixY5g/fz7eeecdOoGmpfKPUfLLly9j1qxZ0Ov1WLVqFUaNGtWoAS86nQ7p6en46quvcOHCBXh6euLDDz/E8OHD4erqatesqgcPHuD48eNIS0tDZmYmCgoKoNfr4ePjg+joaMTGxiIiIgIhISG0CU4lg1DlmqkKMlQdOQ6HQ1s45E9hqVarFTabDXK5HHl5ecjJyUFaWhquXbuG/Px8cLlc+Pn5oX379oiNjcULL7yALl26NKki2Gw2lJSUYP369di7dy9ee+01rFq1Cs7Ozg1SdJPJhNTUVEyYMAEBAQFYvXo14uPjm91p+le0eiWndjhZsmQJ9u3bh3//+9949913G3UeWV5ejuPHj2Pz5s2orq5GVFQU3n//fXTu3BlisdguzhqNRoPKykqcOnUKe/bsQUFBAaxWK4RCITp06ID+/fsjOjoaUqmUrjNOKfeTrttsNiM9PR1nz57FwIED/zbijXLmmUwmyGQyyGQyZGVl4dy5c8jIyKCLS0qlUowePRpjxoyBVCptsl1HDQYDbt26hWnTpoEQgoULF2L06NENmkoQQqBUKrFt2zZs3rwZCQkJ+OqrryAQCFpuOawmW6xrJgwGAzl+/Djp0aMH6dy5M0lPT2+0uHSj0UiKiorIp59+SkJCQoivry95++23yd27d+2yBk7FchcXF5MDBw6QESNGED8/P9KmTRvSvXt3MnfuXHLu3Dk6lru+gTU6nY5s2LCBeHh4kM2bN9dbPpvNRsxmM1Gr1eT69etkxYoVpF+/fiQgIIB4eXmRYcOGkf/973+kqKiI6HS6Jgn80Wq1ZM2aNSQgIICMGDGCFBcXNzgewmQykcLCQjJq1CgSEBBAjh8/TjQajZ0ktj+tXsmrq6vJpEmTSFhYGPnyyy+JRqNplKATq9VKrl27RkaNGkUkEgmJjIwkP/zwA6mqqrJbuSa1Wk0SExPJ6NGjiZeXF/Hy8iLTp08n+/btI/n5+USr1RKTyfTMJZa0Wi355ptviFgsJhs3bnwmGW02G7FarcRsNhOdTkdKSkrIoUOHyOzZs0lISAjx9PQkw4YNI4mJiU2iGGazmRQXF5PBgwcTLy8vcujQoQafl+rMfvrpJ9KpUycycOBAcvv2bTtJbH9atZKr1Wpy+vRp4uvrS8aOHUvKysrsXh/NarUSo9FITp06Rfr160fc3d1Jv379yIkTJ4harW7w+ah6b2lpaWTGjBmkQ4cOJDIyksyePZucPn2aFBUVEY1GQywWS4M7L71eT7Zs2UICAwPJjh07GtQWhcViIVqtlpSUlJAzZ86QGTNmkNDQUBIVFUXeeecdcu3atUaNrrPZbESv15Nvv/2WuLq6kiFDhpCioiK7tF1WVkbeeecd4unpSdavX09UKlWzRy0+jlYdDFNSUoKVK1dCqVRi7ty56Nq1q13XpG02GzQaDZKTkzFv3jyUlZWhf//++Pzzz9GtW7cGVS4lhNBz3aSkJKxYsQIpKSnw8fHB3LlzMW3aNHTo0AESiYTe87yh10UIAYfDgZ+fH2JjY+Ht7U1fp1KpRGlpKfLy8pCXl4eioiJUVVVBLpfThR5kMhmUSiUtD+XYo0pABQQEID4+Hr6+vrh79y4uXbqEEydOwMXFBT4+PuDz+Y1S5onFYoEQgrS0NNy9exdRUVGIiIho8HkEAgECAwNx6NAh1NTUIDo6Gl5eXi0uQKZVK/nevXuxd+9ejB8/HmPGjIFEIrHrC2Q0GpGUlIQ5c+ZAp9Nh6tSpWL58Ofz8/Bpc8JEQgqysLKxfvx6fffYZrFYrJk+ejOXLl6Nnz55wcnKy+8vEZDIhlUoRHR0Nb29vun2LxYKqqipkZmZi5cqV+PLLL7F3715kZ2fDarVCrVbj/Pnz2Lp1K/bv3w+z2YyAgIBHQkqpNM6IiAg62+/06dM4d+4cSkpK6DBUezuwGAwGOBwO5HI5UlNT4eTkhBdeeKHBHSNVn47L5eLUqVPg8XiIj49veQ645jUkGgeTyUSysrLI0KFDSVBQELly5QoxGAx2PYfNZiNJSUkkOjqa+Pj4kNWrV5OysjK7OJOqq6vJqVOnSN++fUlwcDCJiYkh+/fvJ+Xl5cRsNjeaSWg0Gsmvv/5KRo0aRQ4fPkwfpzK+1Go1WbRoEWEymYTNZpM9e/aQyspKolQqSXFxMdm6dStxd3cnAQEBZNSoUSQ7O5totdrHnstkMpHKykpy6NAh0qtXLxIYGEj69OlDDh8+TGQymd2vTa/XkyNHjhAfHx/St29fcvPmTbs4YA0GA8nKyiJ9+/Yl4eHhJC8vz+7vWkNpWXaFnTCbzUhKSkJ+fj769euHiIgIu8aGm0wm5OTkYPHixZDL5ZgxYwbefPPNh0a/Z4EQgsrKSuzbtw9Tp05Ffn4+4uLisHXrVgwbNgze3t6NWhLaYrGgtLQUZ86cQVFREX2cGglFIhH8/f3pmHU3Nzc6ws3f3x8vv/wyXnzxRSgUCpw+fRqrVq2CSqV67Lk4HA48PT0xbNgwrFmzBrGxscjNzcXSpUvxyy+/oKqqCmaz2W7XxuVy6Yi8iooK3Lx50y7tczgcBAYGonv37tBoNPjxxx9RW1trB4ntR6tUcoPBgIMHD4LH42H27Nl2Dx2VyWT45JNPUFRUhBdffBGzZ8+Gu7t7g81zk8mEdevW4ThFJmYAACAASURBVOOPP0ZNTQ3ee+89fP755/ReZE0BqVN37c/83XxZLBZjwYIFcHNzg06nw9GjR1FQUPDE71Pz5Z49e+Lzzz/HokWLoFar8fHHH2PdunWoqqqyyzUBv08VXF1d0b9/fxgMBqSnp9PhvQ1tVyAQYMCAAfD09MSBAwfoyrQthVan5EqlEseOHcOtW7cQFxeHdu3a2XWOpNPpcOXKFZw6dQphYWH44IMP4OLi0qBzmM1m5Ofn4/XXX8cPP/wAHo+HLVu24N///jekUmmT7aPNYrEgEokQHBz8TGmmLBaL9kdQYb16vf5vf8fhcODj44NJkyZhyZIlcHd3x44dO7Bu3Trk5+c/y6U88Txjx44Fn8/H7du37aLkwO+dVUxMDLp06YL8/HwkJydDpVI9tqNsDlqdkpeWlmLjxo0Qi8UYMGAAXa/bXlRXV+PQoUPgcDhYsmQJwsLCGtS+zWZDdnY2lixZgsOHD9NlqKji/k0ZLslmszFkyBBs2rQJ/fr1q/fvrVYrKioqYLFYwOFw6I0S/g4qA85qtaJnz54YM2YMjEYjvv/+e6xcuRJ5eXl2UUg2m40OHTogNDQU9+7dg0wms9uUQCwWY8KECWCxWEhKSkJBQUGLUfKWG3D7jJw6dQo5OTkYMmQIoqKi7O6BvnXrFl22uUuXLg1KMiF/bKjw6aef4siRI3BycsKnn36KwYMHN8s2QlTudJs2bZ4p9FSn02HXrl1Qq9UQCoWYNGkS2rRp85e/sVqtuH//Pq5evYqrV68iJycHpaWlAH4P3f3ll19gMBiwevVqBAUFPdN1UTCZTAiFQnTr1g0XLlzAmTNn4OfnZ5dUYx6Phy5duqB3795IT0/HoUOH7JIQYw+aXwI7YbFYkJWVhePHj8Nms6F///7w8fGxW/vkjwL8hw4dgslkwgsvvNDgrW6rqqowZ84cJCUlwdvbG3v37sXAgQMhFAqbJavJbDZj//79GDFiBBITE//2+9Q9MRgMKCgowL59+/DDDz/A398f7777Lj744IMndhbkjy2h9uzZg4kTJ2LRokXYtWsXLl68iJycHDrBxtnZGUePHsU333yDwsLCBl0f5UCMioqCUCjE8ePH7eYkYzAYcHJywuTJk8Fms/Hrr79Co9HAYrHYpf2G0GpGcrPZjJSUFOTk5MDLywv9+vWza04ztbvIrVu34O/vj/Dw8AY59GQyGX744Qf89NNP8PPzw7x589C/f/8mm38/DiqZJy8vD0ql8m+/f+3aNQiFQuTm5uLUqVO4c+cOEhISMHHiRPTq1esv4xKqq6vx22+/YdmyZZDJZI+Y40wmE1FRUXjllVewZcsW7N27F1wuFx988EGDSi+zWCx4eHjAz88P9+7dg1qtfqZ2Hgc1mgcFBSE7OxsXLlzAgAEDmj1DrdWM5FarFZcvX4bJZMLLL78Mb29vu87FDQYDzp49C7lcDi8vrwa1TwjB0aNHsXnzZphMJnz00Ud47bXXmmTHVHtBCAGTyYRSqcTOnTuRmJgItVqN2bNno3///n+p4FarFXv37sWqVatQVlb22Pk2k8lEZGQkhg4dii+//BJSqRQ7duzApk2bGqyYrq6u8Pf3h16vR1lZWYPaqguHw0FAQADCw8NhMBjwyy+/2LUTeVZahZJTVTvS0tLg5OSEf/3rX3YvUmA0GnHjxg3odDr4+flBIBA8k0LqdDrcu3cPGzZsgM1mw/r16zFixIgWsVUum82Gj48PEhIS/nYfNAaDgc6dOyM+Ph4bNmxAYGAgqqqqMHv2bBQVFT3x3mi1Wpw7dw4nTpxA27Zt8dJLL6Fbt24PPS9qaS00NBRubm7o1q0b5s2bB09PT+zZswcpKSnQaDTPfJ3u7u50wZDy8vJnbufPMBgMcLlcxMXFwcPDA7du3UJJSYnd2n9WWoWS6/V6XLp0CeXl5YiKikJQUJDdTSSDwYD79++Dy+Wiffv2z+RQsdlsKCsrw/LlyyGTyTB8+HBMmTLFbjnmDYXNZmP48OHYtm0b+vfv/7ff53K5cHFxQceOHfHee+/B09MTt2/fxubNm1FaWvpY7zLVIc+dOxdffPEFpk+f/lBwDTVdcXZ2puPZ+Xw+RowYgcmTJ0Oj0WDr1q0N8l6LxWJERERAIBAgNzcXVqvVbp5wBoOBHj16wN/fH0VFRbh3755dg3qeheZ/s+yAUqnE999/D7PZjB49ekAkEtldaahqpiKRCB07dnymUZwK0jl06BA6d+6Mt956CyKRqMXEOttsNhQWFuLs2bO0h/vvoEbdsWPHYvLkySCEYM+ePdi3bx9sNtsj33d2dsbQoUPRp08fyOVyfPDBB8jMzERgYCB69+4NPp8PJpNJR9NR53B2dsbrr7+O0aNH4/Lly1i7di2MRuMzKSebzYaXlxeqq6tx7949u69p+/n5oU+fPlCpVLh+/Xqzr5m3CiUvLCxEeno6wsPD0aVLF7tkZP0ZtVqNmpoaevucZ2k/OTkZe/fuhbu7O2bOnImwsDC7ythQLBYLkpOT8dFHH+Hy5cv1+q2zszMmT56Mvn37wmazYdu2bUhPT3+sWW2z2XD06FHMnz8fFRUVGDBgANauXYvy8nIQQhASEoLPP/8c7du3p39D1ZCbPn06wsPDcfHiRWzduvWZvOMcDgdhYWHg8XgoKSnB3bt37eoFFwqFeOmllyAQCJCSkvJEq6apeO6V3Gq14tq1a9BqtejSpQtCQ0PtruCEEKjVaiiVSoSEhMDFxaVe57BYLFCr1fjhhx9QUVGBd999F3Fxcc1W0fRJ2Gw2GAwGVFVVQafTPfL3v3pR2Ww2vL29sXbtWgQHB6OsrAxLly5Ffn4+rUCEEHpOvnbtWhQWFiI2NhaLFi1CSEgI8vPz0aFDB3z88ccYNmzYI34KPp+PDh06YMqUKWAymdi9ezcKCgrqraBMJhM+Pj4IDQ2FXC5HZmamXZWcw+EgKCgIMTExKC0txZUrVxxK/qzYbDao1WrcunULZrMZvXr1gqenp93PQwhBbW0t9Ho9AgIC6j3f1+v1OHLkCJKTk9GjRw/MmjWrxe9O8iQUCgWA3+8J9X8KgUCAbt264Y033qDTL3/88Uf6ezabDampqZg8eTKuX7+Ojh07YseOHYiNjYVCoQCXy8Xy5csxatSoJ640cLlcjBs3DqNHj8bt27dx5syZx3ZIfwWDwQCPx8PIkSNhsViQkpJi93mzUCjE2LFjwWQycerUKbu2XV+eayW3Wq3IycnBgwcPwGazERMT0yilfw0GAyorK0EIgbu7e73n+8XFxfjss88QGBiIqVOnNmjrnsaEy+UiJiYGCxcufGhHU71ej8LCQly8eBEXLlygK7uePXsWKSkpKC4uhtFoBPD7KDlq1ChMmDABALBr1y4sWrQIJ06cwPfff4958+ZBLpdj0KBB+Oqrr+hOk8vl4ttvv0W/fv3+cg2cwWBAKBRi5syZiIuLw48//og7d+7U+1rZbDaGDRsGsViMtLQ01NbWwmq11rudJ8HhcBAZGQmxWIz09HTI5fJmC4x5roNhrFYr8vPzUVFRgaCgIPj4+DRK4IFWq0Vubi4IIfD396/XnF+lUuHIkSPIycnBwoUL0bt37xbhSX8cTCYTXbp0oQs+UNhsNigUChQVFSEmJgYdOnQA8Pt6c0lJCcRiMe0kAwAfHx/MmjULHA6HLuH8/fff48KFC9DpdIiNjcXChQsRGRkJDocDQgiioqLAZrOfKhiIcpxNnToVy5Ytw8aNG+k670/rxGSxWPD29kbXrl1x4MABnD17FiNHjrTbjijUmrmfnx8yMjJw9epVJCQkNE9gTKNnrDciWq2WLF++nAQGBpL58+c3Wq2w+/fvk8GDBxM+n0+uX79er6INKSkpJD4+nohEInLr1q0WWQOMwmAwkBMnTpDp06eTpKQku7RptVrJ6dOniVQqJRwOh/Tq1YsUFhY2uGCD1WolFRUVJD4+noSEhJADBw48sUDFk7BYLGTjxo1EKBSSmJgYkpOT0yCZ6kIVe5w2bRpxc3MjH374YaMUw3gaWuaQ8pQQQnDnzh1wuVwMGjSo0XZDqa2tRUFBAdq1a1fvElJJSUkoLi7GnDlz4Ofn1yLNdAqbzYYHDx7g8OHDDU7xJH/EtScmJmLevHlQKBQYPHgwvvzyS/j6+jZ4RGMwGHBxccGoUaPAYDCwd+/eJxaoeBJMJhPdu3dHXFwc8vPzceHCBbuul7NYLERFRUEsFuPWrVv1ls9ePLdKTu30kZ2dDTc3N3Ts2LHRTKGSkhKo1Wp07NjxqT3iRqMR2dnZ2L9/P8RiMV577bUGJ7Q0NuSPfdQ0Gk2DHFHkT170vLw8xMbGYsGCBbRZ3tDOjtpWePjw4ZBKpbh48SJu3rz5VPnrddsICQnBoEGD6GpCJSUldpubMxgMREdHw8XFBUVFRXaNrqsPz62SWywWFBYWoqKiAoGBgY0SAENx9+5dOpb6aZW8trYW33zzDYqKitC5c2cEBwc36X5gz4o9tiK22Wy4evUqxo8fjxs3biAiIgJ79uxBz5497XoPmEwm2rZti+HDh0Mul2Pfvn2oqampVxsuLi4YNmwYOBwOUlNTcf78ebt62kNCQhASEkLvJGsvS6E+PLdKrtVqcfr0aZjNZoSGhjao/PHfQSl5eHj4U5dhksvlSE5OpjcBpMoNt2R4PB6GDh2KXbt2YciQIfX+PfmjdBRloqvVatpEpyrc2BMqdXTQoEHw8/PDxYsX651wQnUUEyZMgMViwcmTJ+3qBXdyckLfvn1hMBiQmZnZLAkrz62S63Q6JCcnQygU0rHqjREEQxVtdHJyogspPs3vHjx4gPLycrRp0wZxcXEtXsEpPD09ERERUe9CCpSJfvbsWaxduxb379+nTfSuXbs2WoYdk8mkU4tVKlW9I/WosspTp06Fu7s7Lly4gLy8PBgMBrvIx+Px0LNnT7BYLNy7dw+1tbVNPpo/t0qu0WiQnZ0Nb2/vRtu80Gq1ory8HAqFAk5OTnB1dX0qa8FiseD+/ftQqVTo3r37Q+GZLRmTyYTdu3ejf//++PXXX+v1W6vViqtXr+LVV19Feno6OnTogH379iEuLq7RpykeHh4YPHgw2Gw2kpOT661EHA4H7dq1Q58+fVBdXY3vvvvObk4yasNHd3d3lJSUQKvV2qXd+vDcKnl1dTVMJhM8PDzg7u7eKOcwm824desWtFotxGIx3NzcnkrJCwoKkJKSAkII4uPjG83rb2/IH+Wo6ut4s9lsOHz4MObPnw+NRkOb6O7u7k2SfMPhcBAeHg5XV1c8ePCg3pVYqQi4hIQE+Pn54ciRI8jLy7OrfKGhoaiurm5Qiuyz8lwrucVigbu7O9zc3BrlHCaTCTdv3oTFYoGvr+9T721dVFSEW7duITw8HJ06dWqxwS+Pg1r6eprRkBACjUaD06dPY82aNcjNzaUDXaKjo5usTh2LxULbtm0RFBSE2tpaXLp0qd5KzmKx0KlTJ0RFRUGlUiE1NdVuXnY2m43Q0FCYzeaH6tk3Fc/P2/cn5HI5zGYzPDw8Gi0OXK/X48aNG2AwGIiMjHzqUSk9PR0KhQIvv/yy3bdmamxYLBZ4PN5TXavFYsG1a9cwYcIEZGRkoEOHDjhw4ABiY2Ob1HqhCjT26tULZrMZV65cqXc8OwD4+vqiT58+tAWn0WjsMn+mlByAXS2Ep+W5VfLq6mqYzWZ4e3s32gulUChQXFwMiUSC3r17P7WSX716FQKBAC+99FKLXxuvC5/Px8SJE3Hp0iW8+uqrf/ldQgiOHDnyiBe9oTXonxU2m42BAwdCIpEgLy/vmVJQKScZj8dDdnY2MjIy7LKcxmazERQUBAaD0SxK/kRXsclkgkajwY0bNyCTyaDX6yGRSBAcHAyJRAIAyMnJeWLBRKPRiNraWggEAvB4PLsEqlDF+tVqNR48eACLxWL3Wm4UVqsVMpkMpaWliIyMRPv27f92RLZYLJDJZLh9+zakUildYuh5gfyRUltUVAQej/fEaZBWq8WlS5fw6aefIjc3Fz179sSiRYsQHR3dbEULmUwm2rVrh+DgYKSlpaGqqgoBAQH1uv8sFgsBAQHo1asXsrKykJWV9VCizrNCxdrzeDw8ePCAroTTVDx2JCeEQKVSYdu2bZg8eTLu3LmD4OBgWK1WfPDBBxg3bhxmz56NX3755YlLAkVFRfjqq69w4sQJlJeXo7a2FlqtFjqdDnq9HkajESaTCWaz+aGPyWSii+0bDAbodDpoNBqo1Wrk5eXh0KFDmDNnDg4cOADg92SIxlByo9GI3NxcKJVKxMTEQCQS/e2DMRgMOHfuHFQqFQICAiCRSJ6r+bjRaMRvv/2G1157DceOHXvsd0wmE65evYpJkyYhMzMTnTp1ws8//4yYmJhm7dAYDAYEAgF69OgBtVqNmzdv1nsZjFpOGzNmDBgMBjIyMh5b3aa+UFs0CQQCFBQU2LXc1NPwSLdrtVqhVCqxbt06HDx4EPPmzcO4cePg4uICQghiY2OxdetWbN68GS+88MITGy4rK8OPP/6Ibdu2QSAQQCqVQiKR0B/KYUYpAuXw0ev10Ol00Gq1UCqVUCqVqKmpQUVFBWpqamAwGGC1WiEUChEWFoa2bds2yughk8lw4sQJAEBcXNxTOZGMRiOuXr0KQgjatm0LoVD4XCk58P873h73cpM/qsx+8sknqKmpwYsvvkhva9TcJayoIoqRkZEAfveLvPLKK/XeJILNZqNnz54QCoXIysqyizJSSu7s7IyqqiqUlJTA39+/yTrFR7TDZDLh8uXLSExMhNlsRkJCAtzd3elILz6fj9dffx2pqal/KWRwcDAWLFiAnJwc3L9/H5WVlSgqKqJHa4vFQjt5KKjYaeol43A49Mfd3R0RERHw9/dHaGgoPDw84ObmhjZt2jSKIpWUlODatWsIDg5GSEjIU73EZrMZ2dnZEAgEjSZXY0JtaMjhcB65Xq1WiwsXLmDVqlW4f/8+evfujaVLl6Jr164tZkrCZDLpJdX79+8/k/ONqsseEBCAmzdvQi6Xg8/nN2ggYTKZcHJyglAohNVqRVVVFXx9fZ+5vfryiOQGgwGpqamorKyEi4vLI+GiLBYLvr6+GDt2LO7evfvEhtu0aYO3336b3iHTZrNBJpMhLy8PDx48wP3795GXl4eKigrYbDa6J3Z1dYW7uzu8vLwQFBREx/66urqCxWLRudyNOachhCApKQkajQZDhgx56ugvnU6HkpISiEQiBAQENJp8jQWDwYCPjw9iYmIeyg83Go1IS0vDm2++CYVCge7du+Onn35qtKlSQ6DufWFh4TMpObVLaVBQEFJSUpCVlQUvL68GKTn1blO58xqNxi7TgKflEcltNhuqqqpo0/nq1auPeLAFAgESEhJQXV39l43XTXZgMpl05E/Xrl3pEZuan1BKy2QywWQywWKx6CICbDb7oUINjangVqsV1dXVOHv2LB0g8bSFBNRqNfR6PXx9ff92D7CWCJfLxbBhw9C3b1+6vhohBMePH8fKlSshk8nw4osvYunSpZBKpS3SUnFyckJQUBAKCgpQUVGBzp0717sNam4OwC7z57rWkc1mg06na14lp9z9PB4PtbW1+Pbbb8HhcDBgwAA64ov6Tt++ff82K6uuYlK/bckYjUacOnUKxcXF8PLyQufOnZ86KYVScrFY3OJzxx+HzWZDVlYWLl68iL59+yIsLAwXLlzAihUrkJeXh/j4eCxfvpxOF22JODk5ISAgAISQZ97YoDGeG4fDAZvNBiEEer2+SR1vj3TFXC4XPXr0QGBgIIxGIy5fvoy5c+di586dqKyspCOJOBwO4uPjn8rr/DyhVqvx22+/QalUon379vUq3GgwGGAymSAWi59pV9DmhvLHLFu2DGfPnkVqaipmzJiBe/fuISoqCjt27KCTTVoqfD6fnmr8udDk00JNLwHYZWpI5b5TSt7UI/kjSk4FBMyePRshISFgMpmQyWRYvXo1Xn/9dZw8eRIGg4HuiVqTggO/B9ncuXMH7u7ueO211+rlVLJYLLDZbODxeM/tfaFe8OTkZHz44YcoLy/HgAEDsG7dOvj5+bVIE70uLBaLNrWfZU9zKvNQJpPRGW726NSo+HgGgwGdTte8S2hUiOBLL70EPz8/bN++HSdOnIBSqcT58+chk8kwZswYTJgwAX5+fs9VRNffodVqkZmZicLCQsTFxSEuLq5ejiXKz/A8FId4HHV9KCdPngSLxUKfPn2watUqdO7cuUWP4BSUk4vBYNAVZOsDNWe+f/8+JBLJU6+sPA3U7jBNba4/8al5enqiX79+aN++PSQSCQ4dOgSFQoE7d+6goKAA165dw6JFixAaGkoH8nO5XEgkEthsNiiVSvo4n8+Hi4sLHdhis9noZQWRSASlUkkHLrBYLDg7O4PH49FlbKleUCQSgRBCt03tCS0QCOj1daptiUQCFosFtVoNs9kMQghYLBZcXV1p+QghIISAw+HAzc0NlZWVOHDgAEwmE+Lj4+kXXqVS0Q+GzWbD2dkZfD6fjp8HfreAqG17LBYLKisraZmFQiF0Oh0tH4PBgEQiAYfDgUKheMj5SEWZ1a1wwmKx4ObmBqPRCLVaTe8oKhAIIBKJoNFo6BRGNpsNsVgMDocDpVJJv+jUyoXZbIZaraYLIwiFQjg7O0OhUECr1YLNZoPD4cBkMiEqKgqffPIJvLy8IJfL6fVe6v5R95rP50MkEsFgMNDBUSwWCxKJBGw2GxqN5qH75+HhQUdUmkwm+vm6urpCq9VCq9U+9HzrviOU+UzdP6VSSbdBlXamOiMqvkIoFEIoFMJkMqG2tvahd4TNZkOr1dLymc1mPHjwADKZDP7+/lCpVLBYLPT90+v19DVS5aFFIhEd7EU9L+oZqFQq+hlQJrparUZVVRVdqopaXqPuCXXtEonELsVGGOQvuhQqMEKtViMlJQUHDx7E0aNHUVlZSW/8FxwcDLlcDkIIwsPDsWTJEqhUKqxYsQJyuRwAaIdNYmIivv/+e2g0GggEAowbNw6TJk3CqlWrcOnSJVgsFvj7+2PmzJmIiYnBlClTUFZWBjabjW7dumH69OkwGAxYvHgxlEol+Hw+Ro8ejeHDh+P48ePYv38/dDodRCIRPvzwQwQFBeHzzz9HTk4OzGYzpFIp1qxZA7VajWXLltEvU3h4OL788kvs3LkTy5Ytg0ajQUxMDP71r39h2rRpWLduHc6cOQOr1Qpvb2+888476NWrF95880264GFUVBQiIyOxdu1a+jqYTCbGjRuHcePG4ddff0ViYiJqa2vBZDKxYMECdOrUCR999BHKyspgNpvBZrPx3//+F2azGf/5z3/oTtLHxwfffPMNrly5gvXr14MQApFIhCFDhmDKlCnYsWMHfv31VxBC4OPjg/fffx/h4eFYsWIFMjIyAADt27fHF198gdu3b+Prr79GWVkZGAwGhg0bhunTp2PZsmXIyMhAcXExioqK0K1bN7z99ts4cOAAFAoFWCwWXFxc8MUXX6C8vBwrV66ETqeDUChEv379MHXqVJw9exbfffcdLBYL3NzcMG/ePAQHB2PHjh04efIkCCHw8/PDjz/+iIyMDGzZsgX37t0Dk8lEbGwsVq9ejX379mHPnj1QqVTgcDiYOHEiJk6ciJUrVyI5OZlWrKVLlyIwMBArVqxAdnY2nYk2f/58pKenY+7cueBwOIiIiMCwYcMwduxYXLt2Ddu2bYNarYZIJMKiRYvQpk0b7N27F2fOnIHRaKTf6+PHj0Or1SI4OBg8Hg9du3bFqlWrkJSUhG3btkGlUkEgEGDUqFF44403sGXLFjoK08XFBf/5z38QHh6O9evXIzU1FcDvAVYAEBMTQ2+7BQCjRo3Cq6++ihs3bmD79u30/V60aBH69evXYMvwsRFvOp0OPB6P7hXd3NwwcOBAdOrUCXFxcVixYgXKyspw+/ZtlJSUwNXVFWw2G56envSctLKykk68p5IFLBYL3YPxeDx69Far1ZDL5bBareDxeHRPVlVVherqarBYLMjlcrBYLDqYQKPR0D05l8uFRqOBTCajw2ENBgN4PB6qq6vptFQ2m00H2VBykD92AjGZTDh9+jRMJhMCAgKg1+vpEUKpVEIul9OjMKV8ZWVl9IOqqKhAREQE1Go1bYWwWCwoFApwOBzodDrIZDLodDowGAwYDAZwuVwoFAr62qnIPwaDgerqavo8QqEQbDYbJpMJ1dXVtPNGr9eDyWRCoVDQy5kMBoMepevKR21gSBXCoI4rFAp6NKsrR1hYGHr06IFdu3ahpqYGTCaTfrYmkwk1NTV0ZKJGowGbzaafo81mg8VigdlsBpPJhFwup+WjTF9CCGQyGWpqasBgMGgnmdlshlwuh1qtBpvNhtFopOexlMyUxUFZdZR8IpEIPB6Pvn6TyQS5XI7a2tqH3hEqvNpkMoHFYkGpVEImk8FgMMBisdCdhpOTE2pqasDhcKBWq8FkMmGxWGj5KOuNwWBAr9fT8plMJlo+lUpFH6esWI1GA7lcDqVSSesHl8ult6iqra0Fg8Gg37+G8shIrtfrkZycjLCwMAQHBz/yA7Vajd27d+Ojjz6CSqVChw4dsHnzZvj4+EAoFMLd3Z1ea65rEnp4eKC2thZqtZp+kZydnSGRSFBdXf2QOUcF4ZSXl8NsNtNxydRUoO7L6OzsDCcnJ2i1WtoUo8xbNpuNmpoamEwmum1PT09aPipQh8FgoLKyEjNmzIDFYsGGDRvQtm1biMViuLi4oLq6mnaWcDgcWr6KigrauSMQCHD+/HlMmzYNr7zyChYvXgwej0d72ilzjurA3N3dweVyIZPJYLFYaDmkUikIIaiqqqLvOYvFglQqhcFgoF8Yynfi4uIClUpF1w6j5KM6OMok5PP58PT0hNFohEKhoKcZ1DOgXrq9e/dikez+jQAAIABJREFU3bp1WLNmDWbOnImqqip6ysRisej7RykzJYdEIoFer4dCoaDvtZubG22yarVa+v75+PjAaDTS0wnq+Xp6ekKtVkOtVtOmrVgspuWjOsi6908ul9NtcDgcCAQC/Pbbb1i0aBFGjRqFBQsWwMnJCc7OzjAYDFCpVPS74+7uDjabjdraWrrDOnz4MFasWIFevXph8eLFaNOmDdhsNn3/NBoNVCoV3eGLRCJIJBIolUp6MKOmhTweDzU1NfQzWLVqFY4cOYLp06fjtddeg0gkop+Bs7MzfU/qviNCobDBiv7ISG42m3Hv3j2IxeLHKrmTkxNeeukl2nwXCAQICQmh95amAlm8vb3p31APRiQSPeSoo467ubk95IigAl+kUukj3wV+N1/rfhfAI8tW1HEvL69H2maz2Q+1oVKpsGXLFlRXV6N///7o0qULnJycaDnc3NzonHVKjroKSR3n8XhgMpngcrnw9fUFn8+nRy6JRPJQUA0lX91rrHvcz8/vkeOU/+HP96Ru23Xvk4eHx0PyUfNnb2/vh44zGAx4eHjQnUbdYKS6z5GSg8PhPBSWWff51t2kkLoWV1dXOmqQ+i6Px3vo2VAy/9U7UjcrjrqeP+99p9fraQvIw8ODLg32NPLl5+cjMzOTjl/v0aMHnbNAfaj585/lcHFxobMz/3xfqWtksVgghMDFxQXe3t6P3BM2m/3Q87XX7ryPjXirqalBamoqOnToALFY/NCJWCwWRCIRQkNDIRaL4e/vT/fYfxeR9qTllycdf5JX83HHn3TOxx3/8zGqWCOLxUKvXr0eiVV+WrmpCD2LxfJI4M+T5KvPNT7peH2v/XHHWSwWuFwu3bm7urrSo3djyPckORr6LhBCaEeXQCB45O9Pks9msyEnJwfXr1+HUChEnz59HhvoVd93uO41UlafSCSi35W/ux578IiSU862Q4cOISYmBp07d4ZAIKCrbZrNZqhUKty7dw+enp545ZVXnroSJ7UGSyWgUP9SXu66PSbVQ9aNlGusmHWDwQCZTAYnJydER/9/7Z15XFRl+/8/szLALAwMy7AIAsomIipkbrmXa+GWPdWjlmmlqWn6tGp+q5c+ZZqammtaP9e03C01ywVxwR2QkH0bdhhgmPWc+/eHnnk0NbYZhoHzfr14WYyccw/j59zXfd/X9bm6N/kXzaQu6nS6Fk12sBRME8CoqCj4+vraejhNgtlTAmA+L68PZlf9woULyMrKwtChQy1uvklRlPn0paWrE594hKZSqbBgwQIMHToUo0aNQlRUFLhcLlJSUrB//35kZmbi3XffRVxcXIMHbDQaoVKpkJ2djezsbBQUFKCsrAxqtRo6nc58/MOEn8yaWKlUIjQ0FAqFwipPOp1Oh7KyMri5uSEgIKDJDxInJydzOrBarTavuewFJoyWyWR2e9av1WpRVFQEAA02+DSZTKioqDBbfL/33ntQKBQWGxPzEGEiPEussxvDIyIXiUTo2bMn+vbti7q6Oly4cAEbNmyAVCo172aGhYVh2bJliIyMfGIyTFVVFdLS0pCSkoIbN24gLy8PRUVF5vNsrVZrPr8G8MjaDPjf+k8kEkEikcDT0xOdOnVCeHg4unTpAk9PT/PatzkwT1lnZ2dzIkVTkEgkcHR0hFqtRn5+vtWsoq2F0WjEoUOHsG7dOsybN69eC6jWiEajQU5ODjgcToOjEYPBgAMHDiAnJwdRUVHo0qVLg+sVGgKTO8FsYNp8JheJRBg5cqS5GiwuLs58JEUIgUgkatAB/a1bt/DKK6+guroaPB4PTk5O5p+VSqVQKpVQKBRQKBSQyWRwdHSEyWRCVVUV1Go1qqqqoNFozEditbW1KCoqwoULF2AwGODs7Ixnn30Wq1atarbIAVjEkkcqlZoTN3JzcxEbG9vscbUkjGFIcnKy+UzX3tBoNMjOzoZYLH5kU+5xMAUj/+///T9QFIXBgwdb3GWWSZVlZnJmU7eleETkzC7fgzg4OMDBweGhdXN9SCQSdO/eHeHh4ejevTv8/PzMInd0dISjoyMEAsEj9eEP1p/TNG32daurq0NNTQ2Ki4tx9uxZXLhwwXw84eLiYpEiguYiEong5+eHGzdu2MR6l+XeWXR2djaio6Mf2gV/EhRFIT8/H+np6QgICEBsbKzF03cJIdDpdNDr9ead+FaxJn+Q+nbNH0fnzp2xcuVKyGQy8yzeXJi1TXh4OFQqFX7//Xfk5uY2u4iAKWpgkmKamlcsFAoRFhaGy5cvo6CgABRFgcfj2U3IzhgO9u7d2y433h5MlOrcuXODRG40GpGcnAyj0YiOHTsiIiLC4vs+NE2jurranMTj4+PTomYbVnucMMX7rq6uFhE48L/ie19fX7i7u6Ourg55eXnNblAnEong5uZm7kPeVJE7ODigd+/e4HK5yMrKMieA2AsCgQDjx4/HgQMHMGLECFsPp1EwIXFiYiK4XC66d+/eoOIppiiJw7nnrW+Nxow0TUOtVqOurg6urq4tblvduusGHwOHc8+1g9lpLywstIjIFQoF6urqcOvWrSZ3zmAcc9zd3ZGXl2fOjLIXKIpCeno6Dhw4gIyMDFsPp1Ewa+srV65ALpcjMjKyQTN5YWEhUlJSIBQKERUVZZWxMSLX6XTw9/e3yj3+CbsTOQBzJpFQKIRKpbKIyP38/GAwGHD16tUmi5zJn46KikJxcTGSkpKaVO5oK0wmE86dO4dFixaZiyrsBYqizKc4TATZkHVvfn4+0tLSoFAoEBISYrWxMYYrzTmibSp2KXLgXsoiU2jS3E6RfD4fISEh4HK5SEpKanZRf69evUAIwZEjR2zSxbKp0DRtPme2RWO+5mAymfD7779Dq9UiJCSkXmceJukrOzsbhYWFeOaZZ6zm5mMymZCTkwMACAgIsMo9/gm7F3lZWZm5pLWpCAQCREVFQSaToaKiAiqVqlnN7sLCwuDm5oaff/7ZXLBhT9jLRiED44AaHx9vLlutz3uQSX+9c+cOuFwuRowYYVWRM+2RWJE3AiZcLy0tbbbI+Xw+QkND4erqiurqaty9e7dZYXbHjh3Rs2dPlJWV4dq1axbrjmltBAIBoqOjMXv2bERHR9t6OA2GEZFKpYKbmxv69u1bb8Yec6yVnp4OiUSCqKgoiybA/H18WVlZ5k3jlsZuRc44opaUlKCkpKRZsyVTGjhkyBBzDnNTGuYxKJVK9OzZEzweD2fPnrWb0JfP5yM2Nhbz58+3K5FrtVrcvHkT1dXVCA8PR6dOner15mOO2woLCxEQEPDYYhZLwDxMMjIy4OHhYRO7NLsVubOzM3r37o3Kykrk5OSYk2iaw5gxY+Dv74+DBw+a85+bAtOqViaT4fbt20hJSWnWuFoKg8GAM2fOYMGCBTh//ryth9NgysvLcfLkSVAUhX79+jVow42iKFy8eNHs/mKtIy2j0Yj09HQUFRWhc+fOD5WjthR2LfKBAweCy+UiIyPjIQfZptKhQwdMnjwZFRUVOHHiRJP7U3M4HAQGBsLPzw+5ubm4cOGCRR5C1oamaaSnp+Pw4cNmW6vWDkVRKCwsxIULF+Du7o6nn366wT+XnJwMiqLQoUMHq2Wg6XQ6JCQkgMPhIDIy8pHS7ZbAbkXu4OBg3izLzMxEXV1ds9e+Li4uGDx4MDp37oy9e/fi8uXLZteWxiKXy/H888+be4g96HbSWmEKKZjiodYOczbObHAOHz68wZVnNE0jLy/P7MBiLZHX1NTg8uXL5rbf9W0IWgO7FTnjVtqpUycUFRWhpKTEIiLy9PTEqFGjUFRUhOXLl6OioqJJIndxccHcuXMRFhaG5ORk3L171y6E82Adf2uHoiikpqbi999/h4+PDyZMmNCgohTgnsgLCgrMfditJfLMzEwUFhbC19f3EReglsJuRQ7c+wcZGhoKvV6PM2fOWEREjo6OePHFFxEUFISrV69i7dq1KC4ubrTQuVwupFIp/v3vfwMAli9f3uSOHi2FUCjEs88+i02bNmHw4MG2Hs4/whyB7dy5EzU1NRg5ciSCg4MbvLZmElREIpFVRX7r1i1UVVUhICCAFXlT4HK5CAsLAwCcOnXKIiIXCoUIDg7GwoUL4ePjg+3bt+Po0aNNTlHt27cvoqOjcfjwYdy8ebNVz+ZcLhdKpRKxsbGPeLu1NoxGIzIzM3HmzBmIxWJMmjSpwTvXzANCq9VCKBRCIpFYPHJhculTUlKg1WrRvXt3m5mI2LXIeTweAgMD4eLigvj4eLPpvSUYOnQoPv/8c/j6+mLVqlXYtm1bkwTauXNnjBs3Dnw+H7t27XrIhbW1odfrsWfPHgwaNAj79++39XD+kZqaGhw+fBhFRUUYN24cevbs2eBzbkbkhBA4ODhYxamFcQTOzc0Fl8tF3759bbIeB9qAyENDQxEUFASdTofr169bLFecaej48ssvg6IorF27FuvWrUNRUVGjHiR8Ph/9+/fHc889h8TEROzbt+8hR5zWBOPn/mB3j9YGM0PevHkT27dvR0xMDF599dUG+wwy12BOY4RCIRwdHS0ucpPJhNzcXKhUKsjlckRFRdnMUsvuRe7t7Y3w8HBwOBxcvHjRYoknjIXvq6++ismTJ0On0+Hrr7/Gpk2bGr3JJ5fLsXDhQhBCsGPHDqSlpbXawpXWvvFG0zSys7OxfPlyVFdX49VXX23SWpd50DKtlSyNXq/HpUuXUFFRgf79+0MqlbZoeemD2LXIgXtC79q1KxwcHHDz5k2LOrIwVWVvvvkm5s6dC7VajZUrV2L58uWNOpcXiUSIjo7GuHHjkJmZiQ8++KDVbsIxzkCttXupwWDA2rVrkZiYiNjYWMTGxjY6DP7752aNB1pdXR327dsHQghGjhxp04dm6/wkG0lERAS8vb1x584dpKWlWfQ8mjHUf/HFFzFz5kw4OTlh586dWL58OVQqVYOEzviXT5w4Ef3798eff/6J3bt3m1sHtRYcHBzw0ksv4fTp04iLi7P1cB6huroax48fx4kTJ6BUKjF79my4u7s3WUB/twC3FAaDARkZGbhx4wYiIiIQEhLCiry5yOVyDB8+HOXl5eYdbEsKnekkMmfOHLz66qugKApr1qzBhg0bGhW6h4aGYsqUKZBIJNi7dy/Onz/f5GQba1FXV2fuFNqaMBqNyMnJwbfffgudTocZM2ZgwIABTS4qoSgKIpHI3GfOktTV1eHo0aMwGAyIjY1t8Nm9tWgTIndxccHLL78MBwcHJCYmmhvLWRJG6AsWLMBbb72F2tparFmzBt9++22DN9IEAgH69euHOXPmIDMzE6tWrTK3qm0N6PV6HDx4EGPHjsWRI0dsPRwzhBBUV1djyZIluHjxIl588UVMnDixyf55D3qucTgcix+hqVQqnDt3Di4uLujatatNUlkfpE2InMfjwcfHByEhIcjIyEB8fLxVZiLmH8SUKVMwd+5ciMVi7NixA+vXrze3b64PZ2dnvP766xg2bBj++usvvP3228jOzm41QqdpGgaDodWk4DJdRP/73//iypUr6NWrF1588cVm1X4/2F+daYZoKRESQhAfHw+VSoXAwEAEBgbafBOzTYicaTI4ZMgQ0DSNTZs2Wa1VkUAggI+PD+bOnYvp06eDpml888032LdvH9Rqdb1CFwqFcHV1xfTp0xEWFoaff/4Z69evR35+vs3Ddmbv4O+94GwF4wO/efNm7N27F0KhEO+88w6Cg4ObVfvNeK4B9xpRWspnnWlLfPnyZdTU1OCpp55qFUlFbULkwL1wevDgwfD29kZCQgJSU1OtNjsy1sVz587F/PnzUVlZiS+//BI///xzg+7J4XDQp08ffPTRR5BKpdi0aRO2bNkCiqJsKnSmU2vPnj3h4eFhs3EA/ys+WbduHRYtWgS9Xo+lS5fi+eefb3bmGDOTczgcc2dRS8DsG9y6dQsCgQBjx461mttMY2hTIu/atSueeuopAMAff/xh7tltDTgcjjnP/dNPP4VAIMDGjRtx6tSpBhlOcLlcxMTEYNu2bQgICMC2bduwatUqlJaW2kzoAoEAw4cPx4YNGzBw4ECbjAG4F6KXl5fjyy+/xMaNG+Hu7o5PPvnEXFrc3FlXq9WisLAQAB5qh9xctFotjh8/DpVKhd69eyM6OrpV9JRrMyLncrmQyWQYPXo0xGIx4uPjm+Wh3hB4PB4UCgWmTZuGqVOnorS0FF988QWSkpIalDEmFovx3HPP4d1334VUKsWXX36J7du3NzqrzlIQQpCWloajR4/arAMME6Jv3LgR27dvh8FgwLRp0zBu3LgGl5HWR0FBAW7fvg0+n49OnTpZ5JoURUGtVmPHjh0Qi8WYMmWK1dxmGg1pY6hUKjJ9+nTi6upKtmzZQiiKapH7lpaWkg8++IAIhUIydOhQcvv2bULTdIN+1mQyka1btxKJREJcXFzIF198QfR6fYN/3lJoNBqyZs0aIpPJyNq1a1v03gxqtZosWbKEcLlc4uLiQj766COL/h5omiZ79uwhcrmcPP300yQjI8Mi19VoNOT7778nDg4OZPr06aSwsLDFP78n0WZmcgYXFxfMmDEDMpkMZ86cQU1NTYvsXMtkMvz73//GpEmTkJ6ejq+++goFBQUNKmrh8XgYN24cNm7cCH9/f6xbtw6ffPKJTXbdyf0+dC2N0WhEUVERli1bhs2bN8PX1xeLFy/G7NmzLbY7TdM06urqEB8fD5qm8corr1gsXC8sLMTBgwehUCgwcOBAuLq62nxXnaHNiVwkEiEoKAgDBgzA9evXcfbs2RZJ7BAIBAgICMD777+PkJAQnDlzBitXrkRVVVWDhCqVSjFhwgQsWLAACoUCGzduxLJly3Dnzh2rnRT8HQ6HY979t1Rrq/og9+2U09PT8dlnn2HXrl3g8/n48MMP8fLLL1t0A5CiKBQVFSE+Ph5yuRyDBg1q9iYe81BMSEjA3bt30a1bN8TGxlrN+bVJ2DiSsAparZb89NNPJDIyksTGxhKVStWiodO5c+dIbGws4XA4ZOnSpaSmpqZRP3/kyBHi7+9PhEIh6dOnD7l27Rqpq6uz0mj/h9FoJNeuXSNr1qwh169ft/r9mHueOHGC9O7dm/B4PBIVFUUOHTpklXtpNBqyYsUK0qFDBzJ69GhSUlLS7GtSFEVqamrI1KlTiaenJ9m3b1+jP29rw/v0008/tfWDxtJwOBx4eHggNTUV165dQ2BgIIKCglpsp1Mmk8HDwwOJiYm4ceMGHB0dER0d3eCdYW9vbwwcOBA6nQ4pKSk4fPgw9Ho9PD09zUc+1goFXV1dERwcDC8vL6v+vkwmE7Kzs7F27VqsXr0a5eXlGD9+PD744APExMRYPJJguph89tln0Ov1mDhxInr16tXs96jVanHx4kXs3LkTwcHBmD9/fov3H6+PNilyptG7QCDAsWPHUF1djejo6GYVMzQGkUgELy8vyOVy/Pbbb0hPT0fv3r3NiRf1IRQK4eXlhfDwcDg6OuLSpUu4efMmUlJS4O3tDRcXF6tUiplMJpw+fRrr1q2DXC5Hx44dLXp94N7aW6PR4MqVK1i6dCn2798PgUCAN998EzNmzEBISIhVHFSqqqqwd+9eHDlyBOHh4Zg1axbc3d2btfvNnAQsXrwY5eXlmDdvHrp27doqEokewtahhDUpLCwk06dPJ1KplKxevZoYjcYW3/GcM2cOUSgU5LnnniOZmZmNvr9WqyXx8fFkwIABRCwWE7lcTr777juiUqkIRVEWfT8ajYasXr2aSCQSq+yum0wmkp+fT7Zs2UKCgoKIWCwm3bt3J7/99hsxGo0Wvx8DTdPkwoUL5KmnniKenp5k+/btFrlubW0t2bp1K3F0dCQzZ84kRUVFrWZH/UHa5EzOIBAI0KFDB/z6668oKChAnz59IJPJWvTssmPHjsjLy8OpU6cgl8sRERHRqPpnLpcLDw8P9O/fH/7+/qisrMRvv/2GixcvIjc3F3K5HBKJpFHOKE/CaDTi+vXrOH36NIYMGYKYmJhmXQ+4t6Ot0+mQn5+P7du3Y9WqVfjpp58QFhaGt956CwsWLEBkZCSEQqFVoixmR33btm04efIkXnrpJUyZMsUiG26JiYlYuXIlAOCdd95Bly5dWse5+N9o0yLn8/lwcnJCbm4url27hurqavTt29diucoNQSqVQiqV4vfff0deXh46dOiAzp07A2jYupoxcXBzc0NISAh69OhhLoJISEhAYmIiCgsLIZFIzOE7s/Zv7HtkLI6Tk5MxZMgQdO3atfFv+P519Ho91Go1srKysGfPHqxatQqnTp1CcXEx4uLiMG/ePAwcOBA+Pj5W+zzIfZuns2fP4ptvvoFUKsVnn30GPz+/ZoXUFEWhtrYWW7duxdmzZxEXF4cJEyZAKpVacPQWxMaRhNXR6XTkxIkTpEePHsTb25v8+uuvRKvVtugYysvLyeeff04UCgWJi4sjarW62Uk68fHxZOzYscTb25sIBAIil8vJG2+8QY4ePUqys7OJRqMhJpOJ0DTd4BCSoihSWlpKbt++TUpLSxs1HpqmiclkInq9nuTn55M///yT/Oc//yHBwcGEz+cTV1dXMnHiRHLmzJmmvN0modfrybVr10hERATx8PAgH3/8MamsrGz2dbVaLbl48SKJjo4mkZGRpKCggJhMJguM2Dq06Zkc+F+4q1arkZCQgKKiohbdhAPuRRQRERG4efMmrl+/DoVCgaCgoGbtICsUCgwYMAB9+/aFRCJBbm4ukpKScOzYMZw8eRLx8fEoKCgwW1g1ZHZnQuuqqiqIxeJ6LY5pmobJZIJer0daWhqOHTuG9evXY/Pmzfjhhx9w5coV8Pl8jBgxAh9//DEmT56MwMDAFjnloGkaSUlJWLRoEe7cuYORI0di3rx5UCgUzdqwpGkaJSUl+M9//oP8/HzMmDED/fr1a9HosLFwCGlFtiRWJCsrC/Pnz0d8fDzeffddzJw5s8WPOn799VcsWrQIarUaBw4cQOfOnS2yhissLERqaiquXLmC06dPIz09HbW1tXB2doa7uzuCgoLw1FNPISYmBp6enhCJRHBwcDCXlDIPAIPBgJ9//hmbNm3CrFmzzBZQhBBzCyW9Xg+dTge9Xo+qqipcu3YNCQkJSElJQXl5OcrLyyEWi+Hv74++ffuiX79+6NSpU4vWVRuNRhQXF2PhwoU4fvw4unXrhrVr1yI8PLzZ166srMSWLVvwxRdfYMiQIfi///s/i32O1qLdiNxkMiE5ORkTJkyAg4MDVq9ejT59+rRolZBGo8GaNWuwePFifPDBB5g3b57F13EGgwF3797Fvn37cPbsWeTk5KC0tBRarRZ8Ph/+/v4IDQ1FWFgYwsPD4efnBycnJ/B4PBgMBhw8eBBr1qzB3LlzMWHChIdma5VKhdTUVKSkpODOnTvIzs6GRqOBUCiEu7s7fH19ERMTg7i4OMTExNjEZ5xpSbxkyRLs27cPHh4e2L59O6Kjo5u1Dif3M9uOHTuGxYsXo6ysDCtWrMD48eMtOHrr0G5ETgiBWq3G6tWr8cMPPyAwMBDfffcdOnTo0GLnmjRN4/bt25g6dSo4HA4WLVqEMWPGWHSGY0Sp0Wig0WhQWFiIwsJC3Lx5E1euXEFOTg4qKioA3MuZ5/F4EAgE5pmopqYGxcXF8PDwgFwuB0VR5msy3nmEEEgkEnTo0AFRUVGIjY2Ft7c3vL29IZVK4ezsDKFQ2OIJITRNIyMjAytWrMAvv/wCuVyOBQsWYPz48c12f2Fy65locNasWZg2bZrN/dsaQrsROXBvlsvJycGsWbNw48YNzJ49G9OmTYOHh0eLhZJVVVU4ePAgPv74YwwfPhwrV66ESCSyarhHCEFVVRXKyspQXV2N6upqZGdnIzc3F/n5+aipqYFOp4NWq0VVVRW0Wi2cnJwglUrh6OgIkUgEsVgMpVIJPz8/+Pv7w9XVFTKZDHK5vNnr3ObCWFbl5OTgo48+wtmzZ+Hk5IS3334bb7zxhvmIsTnXr6qqwooVK7Bz505ERkZi06ZNcHFxaRX14vVii90+W3Po0CESHBxM/Pz8yO7du4nBYGjRJAaj0UiGDBlCQkJCSEJCQovv9v8TNE0To9HYYiW6zYWmaaLVasmVK1fIwIEDiVgsJmFhYWTHjh2kurraIvfQaDRk//79RCKRkB49epATJ04Qg8FgkWu3BK0nwbYFeeaZZ/Dxxx+DoiisXr0aFy9ebNFGhFwuF6NHj0ZdXR3mz59vM5OIv2M0GpGamopdu3bhr7/+svVw6oWmadTU1ODQoUOYNWsWbt68if79++O7777DqFGjLLInQAjB1atXsWbNGjg5OeGVV15BbGxs60td/Sds/ZSxBTRNk9LSUjJ79mwSGBhIRowYQbKysoher2+x+1+7do2MHj2aSKVSsnHjxhapMqsPrVZLNm7cSIKDg8m2bdtsPZzHQtM0MRgMpKysjFy+fJm8/fbbJDg4mCgUCvLKK6+QjIwMc35Ac9Hr9aSwsJDMmDGDKJVKMmnSJFJQUGCBd9GytMuZnMPhQCaTYebMmYiIiEBiYiJ+/PFHVFVVtciMyuFwEBUVhbi4OAQGBuLixYvIycmx+n3rgzknLykpgUajsfVwHoLcP8LT6XTIyMjA999/j1deeQU//PADHB0d8dZbb+Grr75CYGBgk/3YH4RxdN2wYQOOHTuGoKAgLF261OYGl03BjmIOy8Ln89GxY0e8++67WLhwodmNZNKkSRCJRFbfiONyuejduzc2b96MkydPokuXLujUqZPNmw1yudxW1QuN3D+60mq1SE5Oxi+//IKzZ88iIyMDTk5OmDNnDkaPHo1OnTpZ9DiysrISu3btwsaNGxEcHIwPP/wQSqWyVZ+HP4k2n/H2JBiPcZlMBqVSiV9//RWJiYkICQmBj4+PRWaD+hAKhejQoQMOHTpWS355AAAW6klEQVSE1NRU9O7dG1Kp1GY7tuR+324nJyf069cP/v7+VrkH8ydzHMd8PXhUx2TeqVQqnD9/HqtWrcK3336LS5cuQaPRICgoCIsWLcJLL72EgIAAc1Zfc2EeKCdPnsSaNWtgMpnwzjvvYPjw4RCJRK3m4dcY2tUR2pMoKyvD8uXLsW3bNnh5eWHNmjXo2bNniyRzUBSFhQsXYteuXfD19cV3331ns5pkRmhGoxF8Pr9JY3hQtMz1GDEzR13M14Ptpcj9YpKqqirzcV96ejouXLiAhIQE8Hg8KJVKhIaGYtiwYRg7dix8fHws/v71ej1u3ryJBQsWIC0tDXPnzsXrr79uF+fhT4IVOe5lw5WWlmL58uX48ccfERwcjG+++Qbdu3e3utgIIWbHkj179mDs2LFYuHAhIiIiWjxs1+v1OHfuHPbv34/x48dj8ODBDf7Zv8/ENTU1+Ouvv5CcnIzc3FyoVCqUlJSYe78xX8w/Py6XC4PBAJ1OB4PBAJPJBJqmIRQK0b17d4wZMwaRkZHw8PCAi4sLRCJRgww4GoPBYMCdO3fwxhtvoKioCC+++CIWLFgAuVxu8Xu1JO12Tf4gfD4fSqUS8+bNg06nw969e7Fw4UKsWLECXbp0sWrxAYfDgZ+fH+bNm4e0tDScO3cOEokEc+bMga+vLxwdHVtM7DRNIy0tDfv370d0dPQTRU4IAUVRMBgMqKmpQXl5OdRqNfLz8/HXX38hLS0Nd+/eRXV1NXQ6HUwmk3l5xOPxzFHCg0UzTLMKLy8v+Pj4wM/PD76+vubUW4VCAScnJ6uVpJpMJqSmpmLZsmXIzMzEs88+i9dff93uBQ6wIn8IHx8fLFy4EOXl5fjjjz/w8ccf4+uvv7a6PxyPx0OnTp2wefNmzJo1C/v27UNeXh7mz59vXjZYuof243gwpDaZTI99jdnhzs/Px507d3D16lWzU2lFRQW4XC5EIhHc3d3h5eUFpVIJT09PKJVKKJVKuLq6QiKRwNnZ+aE1Lo/Hg1QqhUKhaFFREUJgNBqRm5uLr776CsePH0dMTAzmzJmD0NDQFhuHNWFF/je8vb2xdOlSc47yRx99hP/+97/moxlrIRAIEBgYiC+//BJff/01jh49iszMTEydOhVvvPGGVfpo/x1mtnV0dHxIaMw6vba2FkePHsWBAweQlpYGtVoNo9EILpeLoKAgvPDCC4iOjkbnzp3h5uYGJycnODk5QSgUmmdxLpf72LJX5v9bemPLYDAgLS0Nc+bMwZ07dzBgwAAsXbrUKv52toJdkz8GQgjS09OxYMECXLx4EdHR0ViyZAm6du1q9cILg8GAwsJCLF++HL/++iuMRiMGDRqEadOmoXPnzpDL5Vbb+TeZTMjKysL169fRtWtXBAYGoqqqCpmZmTh//jyOHz+OzMxM6PV6yGQy+Pv745lnnsGAAQPg7u4OsVgMsVjcarqi/hOEEBgMBty6dQvLli3D+fPn0bt3b3z44YeIioqyj5z0hmLtbBt7xWQykVu3bpFRo0YRNzc3MmDAAHL+/Hmi0WhaJM/dYDCQzZs3k/79+xOZTEZ69epFvv76a5KUlESqqqqITqezWGYXA0VRRKPRkOLiYlJcXEwSEhLI4sWLSVRUFBGJREQmk5HY2Fgye/ZscvDgQYv4ltsCiqKIVqsl169fJ3FxcUQqlZK4uDhy5coVWw/NKrAz+RMg99dqKpUKixcvxrFjx+Dh4YEVK1agX79+Vk+YIYSYS0X//PNPbNiwAUVFRZBIJOjWrRvGjx+PIUOGwNnZ2SImjsC9eveffvoJ3377LcRiMfLz86FWq+Hk5ITevXtj6tSpCAoKglwuh6OjozkMtzfq6upw8+ZNzJ07F7m5uRg8eDCWLFkCX1/f1tX5xEKwIq8HQggKCgrw9ddfY8+ePXBxccFHH32EESNGNLuEsSGYTCZotVqkpKRg9+7dZgsrHo+HsLAwDBs2DGFhYXBzc4ObmxtkMhkcHBweWgM/+AAgD5xfUxQFk8mE2tpa5OXlIT09HT/++CNOnToFiURidpQZOXIkwsPD4enp2aptjuqDoihUV1fj3LlzWLlyJVJTUzF48GAsXLgQoaGhbStEfwBW5A2koKAAa9aswffffw9XV1e8++67GDduHKRSaYvtBtfV1SEpKQk///wzzp07h9TUVBgMBri6uiIoKAidO3dGx44d0aFDByiVSri7u8PNzQ0ODg7gcDigaRp6vR51dXVQq9UoKytDcXExkpOTcf78eaSmpkKj0YCiKEycOBHvvPNOq+mx3VyMRiMqKyuxb98+bNmyBfn5+Rg7dixmzpyJLl262Hp4VoUVeQMxmUyoqanBTz/9hGXLlkGj0WDMmDF4//33ERAQ0CJhK3OEVVdXh5qaGuTn5+PAgQOIj49HVlaWeXZm8s/5fP5Dri/k/vk28/cYpxeapsHlchEYGAgPDw9cuXIFixcvxpQpU+x65magaRo5OTn49ttvsWfPHojFYkybNg0vv/wy3Nzc2sRD7J9gRd5ISkpKcOLECXz33XcoKipCVFQU3nzzTcTExEAqlbbYERC5n8BRVVVltmxKT09HRkYGsrKyUFZWhpqaGtTW1ppr5ZmupUKhEI6OjpBIJHBzc0NwcDC6deuG0NBQcLlcVFZWms+37Rmmqu727dtYv349/vjjD/j6+uL111/HqFGj4Orq2upPASwBK/ImoNFokJiYiPXr1+PMmTPw9fXFjBkz8MILL8DFxaVFilv+CYqizKE4Y+JICAGXy4WTkxPEYjFcXFzg5eX1kGMtY4KYk5MDf39/KJVKm72H5sBELLW1tYiPj8fy5ctx584ddOvWDe+//z5iYmLqtZtuU7ToXn4bgaIootPpSEFBAVm6dCnx8vIiSqWSzJw5kxQUFLSY+UR9YzQYDESn0xGtVmv+0ul0xGAwPLYvXF1dHdm0aRMJDAwkW7dutdHIm4/RaCQlJSVkyZIlxNvbm7i5uZHJkyeTzMxMotVq7cbaylK0/VjFCnC5XDg4OMDDwwOvv/46XF1dsXXrVhw4cAAFBQWYOnUqevToAS8vL5vVhzOZZY2BEAKtVmue/e0NmqZRWVmJxMREbNu2DZcuXYKbmxvGjx+P1157DUql0ub1+raAFXkz4PP5cHd3x/Tp0xEQEIDNmzfj9OnTyMjIwMiRIzFlyhT4+vpa3Y3VUjBprfaQsfYgTNpteXk5du/ejd27dyMnJwc9e/bEa6+9hmHDhkEikdh6mLbD1qFEW0Gn0xGVSkW2bt1KQkJCiJubGwkICCA7d+4kVVVVth5eg9Dr9eTQoUNk4sSJ5OjRo7YeToPRaDTk+vXrZNiwYUShUBBfX1+ybNkyUlBQ0C7D87/DbrxZEOZ4Kzk5Gdu2bcNvv/0GkUiEYcOGIS4uDlFRUZBKpa12lqQoClqtFiUlJZDL5ZDL5bYe0hNhOqcy5bl79uxBTk4OunTpgilTpmDQoEGQyWRt/nisIbAitxKFhYU4fPgwfvzxR2RmZsLf3x/PP/88xo4dC19fX3NKaGtaH5pMJqSkpODKlSvo1asXIiIibD2kR2BKYWtra3Hq1Cns3r0b165dA5/Px9ixY/Gvf/0L3bt3t/UwWxe2DSTaLiaTidTV1ZGcnBzyySefEF9fXyKXy0mPHj3IgQMHSEVFRasLI+vq6si6deuIl5cX2bhxo62H8wgURZG6ujqSkJBARo8eTWQyGfHy8jIXl6jVartqetBStM64sQ3A1GV7eXlh9uzZ6NOnDw4ePIirV69iwYIF6NOnD8aMGYP+/ftDLBZDKBTafFYn9xNsNBpNizab+CeYLL+amhokJyfj2LFjOHXqFHQ6HZ577jmMGDECgwcPNmeu2aPRorVhRW5lhEIhFAoFnn32WURHR+PSpUvYsWMHTpw4gRs3bmDo0KEYOnQounTpAolEAqFQaDNLZA6HA4FAAKlUatNqLCbtVq/XQ6vVIikpCSdPnkRCQgKSk5MRGRmJmTNnYsCAAfDx8WHX3fXArslbkAeNDs+cOYPVq1fjxo0b0Ov1CA8Px5QpUzB48GB4eHhALBa3+PiYNfmlS5fw9NNP26Rwg9x3TC0vL8fZs2exZcsWXL58GY6OjvD29sa0adMwduxYc0pqezz3biysyG1EdXU1ioqKEB8fjzNnziApKQmVlZXw8vJCz5490b17d/To0cNs5igQCKw+u1MUBZ1Oh4qKCkilUshkMqvej8FoNEKv10OtVuP69eu4cuUKEhISkJWVBYFAgIiICPTv3x+DBw+GUqmEWCy2e3PFloQVuY0h9+vVb926hSNHjuDUqVOorKyEs7MzIiIiEB0djT59+pjDeQcHB/D5fHOtuCUxGo04ffo0Dhw4gIkTJ2LgwIEWvT7wsCEkY8Gcm5uLCxcu4PLly7h16xZUKhUEAgF69eqFCRMmICYmps0aOrQErMhbAYwHuclkQn5+Pnbs2IE9e/agoqLCXFzi5+eHUaNGIS4uDh06dICrqyucnJwsOg6tVoutW7fi008/xeeff44ZM2ZY9PrAvQdJdXU1VCoVzp07h59++gk3b96ETqeDQCCAXC5Hr169MHPmTERGRsLR0fGx5hcsDYfdeGsFMC4uQqEQAQEBmD17NsaMGYOkpCQkJycjJSUF6enp2Lt3Lw4fPoyAgACEhoaiY8eOCAoKQmBgIJRKpbmMtKmhLDPL6vV6UBTVrPfEpJoyZ9r5+fnIyMhAeno6kpKSkJ6ejoqKClAUhfDwcISGhiIyMhLh4eFmp5sHa+FZmg4r8laGUCg0Wzn16NED1dXVyMvLQ1paGhITE3HhwgXcvn0bV69ehVAohKenJzw9PdGxY0d06dIFkZGR6NixozmsZ0L7B2fDJxWvPOiZ/qQogfytBRLz34wZBROGq9VqpKam4vbt20hOToZKpUJRUREqKytBURQ8PT0xaNAgPP3004iIiEBAQAC8vLys/ettl7DheiuHERPzZTKZkJ6ejj/++APnzp1DZmYmKisrzd1KmLbMXbp0QVhYGMLCwhASEgKFQgFnZ2c4OzvDxcXlsetbpl1vaWkp3N3dH5vWymySabVaaLVa6HQ6aLVaVFVVITc3F2lpaTh//jxu374NjUYDHo9nvqe7uzu6d++O4cOHo2fPnpBIJOYHTlOq5lgaBityO4Pc9wvXarXQaDQoLy9HXl4e8vPzkZWVhYyMDGRnZ0OtVputoHg8HpycnCCTySCXy/Hee+8hLCwMMpnsIWFRFIWKigrk5ubCx8fnoZmV6fa5a9cuJCQkoLq6GtXV1aitrYVGo4FWqzWfbwsEAiiVSvNSwt/fH35+fvD29oZMJoNYLDabTbJYH1bkbQSaplFbW4vS0lIUFxejsrISKpUKeXl5yM3NRV5eHnJycpCXl4fo6Gh88sknGDJkyEOJJHq9Hr/88gs2bdqEmTNnYuzYsQ+9lpiYiGnTpiE7O9tc/OHi4mJeMnh6esLLywuhoaHw9vY2t0USiUS2+JWw3Iddk7cRuFwuJBIJxGIx/P39H2oJzPxZUVGB1157DdeuXcPVq1fxzDPPPCRyxjbq+vXrKC4ufuj6Wq0WR44cQWVlJUaPHo33338f/v7+5qSdv7c8elwrJBbbwIq8DVFfPzFnZ2d06tQJiYmJyMrKeuIO+uOCO71ejzNnzkAkEqFv374ICQmBo6Mju462A9hPqB3B4/Hg5+cHHo+HsrIy0DT9yOtyuRzh4eFQKBQPvVZbW4vc3FzIZDIEBgbCwcGBFbidwM7k7QgulwsPDw/w+Xxz3/AHcXBwwEsvvYSJEyc+tClGCEFVVRWMRiPc3Nzg5+fHhuF2BPsobkdwuVwoFAoIhUIYjcZHRG4ymXD37l3s27cPaWlpD73GdFaRyWTw9PRkZ3E7gv2k2hGMyAUCwRNFfu7cOSxevBiXLl0yf58QAp1OB0KI+cybxX5gw/V2BJfLNZsrPE7kzFl4cXExNBrNQ6/p9XrQNA2JRMIeidkZ7EzejuBwOHB1dYVAIIDBYHhE5E+yZCb3/dgJITapc2dpHqzI2xEcDsfchfVxMznTDnnSpEno3LnzQ68xGW2syO0PNlxvR3A4HPD5fIjFYlRVVT0icoFAgL59++Kpp556pJKNOYNnEyTtD3Ymb2cQQmA0Gh9bEGIwGPDbb7/htddew8mTJ83f53A4cHR0BIfDQW1tbUsPmaWZsCJvRzBr67q6OrNh5INQFIWsrCwcO3YM2dnZD73GZLfV1tays7mdwYq8HUHTNMrLy2E0GhttLuHg4AAOhwONRgODwWDFUbJYGlbk7QiaplFSUgKDwQCBQPDITM6YRjB9yxk4HI45jbWmpgbl5eXsbG5HsBtv7QiaplFcXAy9Xv/YmZzP52PcuHGIiYmBUql86DVnZ2dwuVxUVVWhqKgInp6ebD24ncCKvB1B0zSKiopgMBgeuybn8/lwdXWFq6vrQ9/ncDhwcXGBQCBARUUF8vPz0bVr15YcOkszYMP1dgRFUcjPz4fRaIREImnUmlwsFiMgIABqtRpZWVmPVLCxtF5YkbcjaJpGQUEBhEIh/P39GxVuOzg4oF+/fgAAlUrFityOYMP1dgQhBG5ubujWrRt69uzZqD7pIpEIzz33HP766y+2QMXOYD3e2hEmkwklJSXQarVwcXGBXC5vcMkoTdOoq6tDaWkpHB0d4eHhwZab2gmsyNsRjD+6Xq9/Ymtixj6Kx+OBz+dDIBCwBhF2DhuutyOMRiOKi4uRkJCAwsJC0DT9iOkil8uFi4sLpFIpAgICEBwcbO77zYrdPmFn8nYETdMwGAy4ffs23n//fdy5cwceHh4YOXIk+vXrB4VCgdLSUiQlJeH3339HeXk5PDw8MHnyZAwaNAiurq5siG6H8D799NNPbT0IlpaBqUKjaRrJycm4ePEivLy8sHLlSoSEhMDLywsdOnRAREQEunXrhry8PCQkJCA+Ph4VFRUIDg6Go6NjozbsWGwP+2m1QxwdHeHi4gIejwepVPpI9pqTkxPc3d3h6+sLd3d3bN68GRs2bIDBYMB7770HpVLJhu52BBt7sTwRDw8PzJ8/H//6179gNBrxww8/YOfOndDr9Wzuuh3BipzliQgEAri7u2PSpEkICwuDWq3GgQMHcOPGDTYZxo5gRc7yj3A4HAQEBCA2NhY8Hg+pqak4d+5cs/uXs7QcrMhZ6sXNzQ2dOnUyl5oWFBSwIrcjWJGz1ItAIICfnx+EQqG5KSIbrtsPrMhZ6oXD4UAoFJqNHGtqaliR2xGsyFnqhRACk8kEQoj5rJ3FfmBFzlIvWq0WGRkZZtsoPz8/Vuh2BCtylnopKyvDnTt3QFEU3NzcEBISwlo/2RGsyFnqJSsrC5cuXQJFUejWrRueffZZdia3I9hPiuWJGAwGlJaWYs+ePcjJyYFcLscLL7wAPz8/tlDFjmBF3g6haRo0TYMQApqmQVHUQ22QmO+VlZVh/fr1OH78OJydnTF58mQMGzasUd5wLLaHFXk7RK/Xo7y8HDRNQ6fToby8HGKx2NztVK1WIyMjA1u3bsWZM2egVCrx2muvYdy4cZBKpbYePksjYevJ2xFarRbZ2dm4fv06vv/+e2RkZMDDwwODBw+Gh4cHpFIpqqurUVxcjMLCQgiFQnTq1Al9+/ZFaGgoZDIZG6bbIazI2xE6nQ4FBQUoKCiAWq1+7N9huqi4uLjA09MTSqWS3Um3c1iRtyMYjzeTyfTEjDWmTpzH45m93tjacfuGFTkLSxuHXWCxsLRxWJGzsLRxWJGzsLRxWJGzsLRxWJGzsLRxWJGzsLRxWJGzsLRxWJGzsLRxWJGzsLRx/j8dOkGiaJKAFgAAAABJRU5ErkJggg==)
The maximum value of
to produce a maxima at D is given by
physics-General
physics-
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed
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)
The maximum intensity produced at D is given by
A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed
![](data:image/png;base64,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)
The maximum intensity produced at D is given by
physics-General